Modern Physical Methods in Biochemistry, Part B (New Comprehensive Biochemistry)

MODERN PHYSICAL METHODS IN BIOCHEMISTRY, PART B

New Comprehensive Biochemistry

Volume 11B

General Editors

A. NEUBERGER London

L.L.M. van DEENEN Utrecht

ELSEVIER AMSTERDAM. NEW YORK . OXFORD

Modern Physical Methods in Biochemistry Part B

Editors

A. NEUBERGER and L.L.M. VAN DEENEN London and Utrecht

1988 ELSEVIER AMSTERDAM * NEW YORK . OXFORD

0 1988, Elsevier Science Publishers B.V. (Biomedical Division)

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the Publisher, Elsevier Science Publishers B.V. (Biomedical Division), P.O. Box 1527, loo0 BM Amsterdam, The Netherlands.

No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, neghgence or otherwise, or from any use or operation of any methods; products, instructions or ideas contained in the material herein. Because of the rapid advances in the medical sciences, the Publisher recommends that independent verification of diagnoses and drug dosages should be made. Special regulations for readers in the USA. This publication has been registered with the Copyright Clearance Center, Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which the photocopying of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the Publisher.

ISBN 0-444-80968-6(volume) ISBN 0-444-80303-3 (series) Published by: Elsevier Science Publishers B.V. (Biomedical Division) P.O. Box 211 loo0 AE Amsterdam The Netherlands Sole distributors for the USA and Canada: Elsevier Science Publishing Company, Inc. 52 Vanderbilt Avenue New York, NY 10017 USA

Library of Congress Cataloging-in-PublicationData (Revised for volume 11 B) Modem physical methods in biochemistry. (New comprehensive biochemistry; v. 11 A, B) Includes bibliographies and index. 1. Spectrum analysis. 2. Biochemistry-Technique. I. Neuberger, Albert. 11. Deenen, Laurens L.M. van. QD415.N48 vol. 11 A, etc. 574.19’2 s [574.19’283] 85-4402 [QP519.9S6] ISBN 0-444-80649-0 (v. 11 A) 0-444-80968-6 (v. 11 B) Acknowledgment Many illustrations and diagrams in this volume have been obtained from other publications. In all cases reference is made to the original publication. ThejuN source can be found in the reference list. Permission for the reproduction of this material is gratefully acknowledged.

Printed in The Netherlands

Preface

In the former series of Comprehensive Biochemistry the contributions of physical methods to biochemistry were considered in volumes 1-4, a section which was devoted to the physicochemical and organic aspects of biochemistry. In 1962 the series editors M. Florkin and E.H. Stotz emphasized the importance of these basic sciences for the future progress in the life sciences. Since that time, the application of physical methods to biological problems has solved many questions and opened new avenues of research. Volume 11,part A, of the present series contained chapters on protein crystallography, nuclear magnetic resonance spectroscopy, electron spin resonance, mass spectroscopy, circular dichroism and optical rotatory dispersion. In this volume the range of spectroscopic techniques is extended to chapters on fluorescence and Raman spectroscopy. One chapter deals extensively with neutron and X-ray solution scattering techniques, and a choice of rapid reaction methods is discussed in a further chapter. The use of electron microscopy has been another very important development in the biological sciences and the results are illustrated by a chapter with emphasis on biomembranes. The New Comprehensive Biochemistry series contains a volume (8) devoted to separation methods. This area is now supplemented by a chapter in the present volume on high performance liquid chromatography of nucleic acids and a chapter on reversed phase HPLC of peptides and proteins. The editors hope that the publication of this volume may serve the needs of many biochemists and thus contribute to further research in the biological sciences.

A. Neuberger L.L.M. van Deenen

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Contents

Preface

V

Chapter I Fluorescence spectroscopy; principles and application to biological macromolecules J.R. Lakowicz (Baltimore, MD, USA)

1

1. The phenomenon of fluorescence 2. Factors affecting the fluorescence emission 2.1. Solvent polarity and viscosity 2.2. Emission spectra of melittin 2.3. Quenching of fluorescence 2.4. Fluorescence energy transfer 2.5. Fluorescence anisotropy 3. Time-resolved fluorescence spectroscopy 3.1. Resolution of the emission spectrum of liver alcohol dehydrogenase 3.2. Pulsed lasers for time-resolved fluorescence 3.3. Frequency-domain resolution of protein fluorescence 3.4. Anisotropy decays of protein fluorescence 4. Harmonic-content frequency-domain fluorometry 5. summary

1 4 4 6 7 9 11 13 15 18 19 21 23 25

Acknowledgements References

25 26

Chapter 2 Raman and resonance Raman spectroscopy P.R. Carey (Ottawa, Ont., Canada)

27

1. 2. 3. 4. 5. 6. 7.

Introduction The units used in Raman spectroscopy A model for Raman scattering based on classical physics Raman and resonance Raman scattering: a quantum mechanical interpretation Polarisation properties of Raman scattering Basic experimental aspects Raman studies on biological materials 7.1. Proteins 7.1.1. Amide I and amide I11 features 7.1.2. Side chain contributions to the Raman spectrum 7.1.3. Applications 7.1.4. UV excited resonance Raman spectra of proteins

27 29 31 34 37 38 40 40 40 42 43 43

...

Vlll

7.2. Proteins containing a natural, visible chromophore 7.3. Resonance Raman labels 7.4. Nucleic acids 7.4.1. The purine and pyrimidine bases 7.4.2. Conformation of the (deoxy)ribose-phosphate backbone 7.4.3. Resonance Raman studies of nucleic acids 7.5. Viruses 7.6. Lipids and membranes 7.6.1. The C-C stretching region between 1050 and 1150 cm-' 7.6.2. The C-H stretching region between 2800 and 3000 cm-' 7.6.3. Deuterated lipids as selective probes 7.6.4. Lipid protein interactions and natural membranes

44 48 50 50 52 53 54 56 57 57 58 59

References

61

Chapter 3 Rapid reaction methods in biochemistry Quentin H. Gibson (Ithaca, NY, USA)

65

1. Introduction 2. Continuous flow 3. Stopped flow 3.1. Miscellaneous stopped-flow devices 3.2. Relaxation methods 3.2.1. Flash sources 3.2.2. Observation light sources 3.2.3. Light detectors 4. Combinations of flash photolysis with other techniques 5. Temperature jump 6. Miscellaneous methods 6.1. Time-resolved resonance Raman spectroscopy 6.2. Competitive methods 7. Data reduction

65 65 69 71 72 73 75 75 76 76 77 77 78 78

References

83

Chapter 4 High performance liquid chromatography of nucleic acids M. Colpan and D. Riesner (Dusseldorf, FRG)

85

1. Introduction 2. Techniques 2.1. Size exclusion chromatography 2.2. Anion-exchange chromatography 2.3. Reversed phase and hydrophobic interaction chromatography 2.4. RPC-5 and other mixed mode chromatography 2.5. Sample preparation and recovery 3. Applications 3.1. Oligonucleotides 3.2. Natural RNA 3.3. DNA fragments 3.4. Plasmids 4. Concluding remarks

85 86 86 88 91 94 95 96 96 98 99 101 102

Acknowledgements References

Chapter 5 Reversed phase high per,,rmance liquid chromatography of peptides and proteins M.T.W. Hearn and M.I. Aguilar (Clayton, Vic., Australia)

103 103

107

1. Introduction 2. Retention relationships of peptides in RP-HPLC 3. The relationship between peptide retention behaviour and hydrophobicity coefficients 4. Bandwidtb relationships of peptides in RP-HPLC 5. Dynamic models for interconverting systems 6. Conclusion

107 111 120 126 131 139

Acknowledgements References

139 140

Chapter 6 X-ray and neutron solution scattering S.J. Perkins (London, UK)

143

1. Introduction Part A: Theoretical and Practical Aspects 2. Theory of X-ray and neutron scattering 2.1. Scattering phenomena and their angular ranges 2.1.1. X-ray scattering 2.1.2. Neutron scattering 2.1.3. Scattering angles, vectors and resolution 2.2. The scattering event and the Debye equation 2.3. Scattering densities and allowance for solvent 2.3.1. Concept of scattering densities 2.3.2. Scattering densities and volumes 2.3.3. The contrast difference A p 2.3.4. Mean macromolecular scattering densities p 2.3.5. Scattering density fluctuations pF(r) 2.4. The Guinier plot: Z ( 0 ) and R , 2.4.1. The innermost scattering curve 2.4.2. Cross-sectional and thickness Guinier analyses 2.5. Analyses of I ( 0 ) values 2.6. Analyses of R, values 2.7. Non-uniform scattering densities and contrast variation 2.7.1. The Stuhrmann plot 2.7.2. Solvent penetration and exchange effects 2.7.3. Isomorphous replacement 2.7.4. Matchpoints of multicomponent systems 2.8. Label triangulation 2.9. Wide-angle scattering and modelling strategies 2.9.1. Spheres and ellipsoids 2.9.2. Scattering curves at large Q 2.9.3. Independent parameters from scattering 2.9.4. Debye curve simulations 2.9.5. Interparticle interference 2.10. Distance distribution functions

143 144 144 144 144 145 146 147 149 149 150 152 154 154 160 160 162 163 165 167 167 170 172 173 173 175 175 177 178 178 180 180

X

3. Experimental practice and instrumentation 3.1. Sample preparation and measurement 3.1.1. Sample monodispersity and concentrations 3.1.2. Sample assays 3.1.3. Sample backgrounds 3.1.4. Sample holders 3.1.5. Instrumental calibration 3.2. Labelling techniques and deuteration 3.3. Sources of X-rays and neutrons 3.3.1. Anode sources 3.3.2. Synchrotron radiation 3.3.3. Reactor neutron sources 3.3.4. Spallation neutron sources 3.4. Scattering instrumentation 3.4.1. X-ray cameras 3.4.2. Neutron cameras 3.5. Data reduction Part B: Biochemical Applications to Proteins, Carbohydrates, Lipids and Nucleic Acids 4. Applications of X-ray and neutron scattering 4.1. Introduction 4.2. X-ray studies on globular proteins 4.2.1. Relationship between R , and M , 4.2.2. Comparison of crystal and solution structures 4.2.3. Conformational changes and ligand binding 4.2.4. AUostericism 4.2.5. Molecular modelling of proteins 4.2.6. Associative systems and time-resolved synchrotron radiation studies 4.2.7. Interparticle interference 4.2.8. X-ray contrast variation and anomalous scattering 4.2.9. Label triangulation of heavy metal probes 4.3. Neutron studies on globular proteins 4.3.1. Contrast variation studies 4.3.2. Label triangulation and deuteration 4.4. X-ray and neutron studies on glycoproteins 4.4.1. Plasma glycoproteins, proteoglycans and polysaccharides 4.4.2. Immunoglobulins 4.4.3. Components of complement 4.5. Lipids, detergents, membrane proteins and lipoproteins 4.5.1. Lipid vesicles and complexes with proteins 4.5.2. Detergent micelles and complexes with proteins 4.5.3. Lipoproteins 4.6. Nucleic acids and nucleoproteins 4.6.1. DNA studies by X-ray scattering 4.6.2. X-ray and neutron studies on transfer RNA 4.6.3. Protein-nucleic acid interactions by neutron scattering 4.6.4. Chromatin and chromosomes by X-rays and neutrons 4.6.5. Ribosomes and their constituents 4.6.6. Viruses 5. Conclusions Acknowledgements References

182 182 183 183 184 184 185 186 187 187 187 189 190 190 190 191 193 194 194 194 194 194 196 196 198 199 201 203 204 207 208 208 21 1 213 21 3 218 219 221 221 224 226 230 230 231 234 236 239 244 249 25 1 251

Chapter 7 Electron microscopy W.F. Voorhout and A.J. Verkleij (Utrecht, The Netherlands)

267

1. Introduction 2. Negative staining and metal shadowing 2.1. Negative staining 2.2. Metal shadowing 3. Thin sectioning 4. Low-temperature techniques 4.1. Cryofmation 4.2. Freeze-fracturing 4.2.1. The freeze-fracture technique 4.2.2. Biological membranes 4.2.3. Lipid phase transitions and lipid polymorphism as visualized by freeze-fracturing 4.3. Localization studies 4.3.1. Introduction 4.3.2. Immunocytochemistry 4.3.3. Marker system 4.3.4. Cryo-ultramicrotomy 4.3.5. Cryo-fractures 4.3.6. Label-efficiency 5. Conclusions

261 268 268 269 210 212 212 214 214 215 219 286 286 281 288 289 290 293 295

Acknowledgements References

295 295

Subject index

301

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A. Neuberger and L.L.M. Van Deenen (Eds.) Modern Physical Methoak in Biochemimy. Part B 0 1988 Elsevier Science Publishers B.V. (Biomedical Division)

1

CHAPTER 1

Fluorescence spectroscopy; principles and application to biological macromolecules * JOSEPH R.LAKOWICZ University of Maryland at Baltimore School of Medicine, Department of Biological Chemistry, 660 West Redwood Street, Baltimore, M D 21201, USA

1. The phenomenon of fluorescence Luminescence is the emission of photons from electronically excited states. Luminescence is divided into two types, fluorescence and phosphorescence. In phosphorescence, the emission is from an excited triplet state to a ground state singlet. Since this transition is forbidden the rate of return to the ground state is slow, which means the decay times are long (msec to sec). Fluorescence is the emission from excited singlet states, also yielding a ground state singlet. These allowed transitions to occur rapidly, with rates near lo8 sec-'. Consequently, the decay times for fluorescence are typically near lo-' sec or 10 nsec. In this chapter we will discuss primarily fluorescence, but the concepts are also applicable to events on a slower timescale if the phosphorescence is observed. The nanosecond timescale of fluorescence provides much of its usefulness in biophysical chemistry. In solutions near room temperature, a variety of molecular events can occur within 10 nsec and alter the emission. These events include rotational diffusion, collisions with quenchers, solvent reorientation, and energy transfer. These events alter one or more of the spectral observables, and can thus be detected by analysis of the emission. Substances which display fluorescence are generally delocalized aromatic systems with or without polar substituents (Fig. 1).It is difficult to predict which molecules will be fluorescent or non-fluorescent because exceptions can usually be found. However, several general rules are generally true. Rigid molecules are usually more fluorescent, or at least their fluorescence more predictable, than molecules with the possibility of internal rotation. Hence, perylene and anthracene fluoresce with high efficiencies, whereas stilbene can be much less efficient. In viscous solvents, in which rotational reorientation to cis-stilbene cannot occur, trans-stilbene is highly fluorescent. In non-viscous solution stilbene is only weakly fluorescent. This illustrates an important aspect of fluorescence, which is that the excited states are involved, * Dedicated to Professor Gregorio Weber on the occasion of his seventieth birthday.

2

Perylene

Anfhracene

I ndole

P PO

trans- Stilbene

2-Naphthol

Fig. 1. Typical fluorescent molecules.

and these states have a different electronic distribution which may alter their chemical properties. In the excited state trans-stilbene (Fig. 1) isomerizes to the non-fluorescent cis-stilbene. The altered electronic distribution can also alter chemical reactivity. For instance, the pKa of the hydroxyl group on naphthol decreases from 9 to 2 upon excitation, presumably as the result of transfer of electron density from the oxygen into the aromatic ring. The emission from an aqueous solution of naphthol can be due to unionized naphthol, naphtholate, or both, depending upon pH and the concentration of basic species available to accept the dissociated proton. The presence of substitutes for carbon in the aromatic system generally alters the emission from the aromatic nucleus. Insertion of oxygen or nitrogen into the ring system often results in good fluorescence. Hence, indole, fluorescein, PPO, the rhodamines and similar substances are fluorescent (Fig. 1). The presence of sulfur, nitro groups or heavy atoms like iodide generally result in quenching of fluorescence. Biological systems contain a variety of intrinsic (natural) fluorophores (Fig. 2). In proteins, tryptophan is the most highly fluorescent amino acid, accounting for 90% of the emission from most proteins. Emission from tyrosine residues is also observed, especially in proteins lacking tryptophan, in denatured proteins, or in those with a high ratio of tyrosine to tryptophan. Tyrosine is highly fluorescent in solution, but its emission is often quenched in native proteins, due either to the quenching effects of hydrogen bonding to the hydroxyl group or because of energy transfer from tyrosine to tryptophan. The emission of phenylalanine from proteins is less studied. The nucleotides and nucleic acids are generally non-fluorescent. However, some notable exceptions are known. Phenylalanine transfer RNA from yeast (tRNAPhe) contains a single highly fluorescent base, called the Y-base, whch has an emission maximum near 470 nm. The presence of this intrinsic fluorophore has resulted in numerous studies of tRNAPheby fluorescence spectroscopy. Regarding the “nonfluorescent” nucleic acids, it should be noted that they do fluoresce, but with very low yields and with short decay times.

3

CH

/I

CH

I

CH

II

CH

I

CH

II

ANS

DNS-CI

DPH

-ATP

Ethidium Bromide

Acridine Orange

Fig. 2. Intrinsic biological fluorophores. For NADH and FAD we only showed the fluorescent part of the molecule.

Other natural fluorophores include NADH and FAD, whose fluorescent moieties are shown in Fig. 2. In both cases the amount of fluorescence depends upon their local environments. For instance, the emission of NADH is usually increased about three-fold upon binding to proteins, whereas the emission of FAD is usually quenched. C02H

C02H I

a;H2 6 H2N-CHI

H

Tryptophan

Y,- b a s e

H2N-CH

I

C02H

I

H 2N-CH

6 I

\

OH

Tyrosine

NADH

Phenylalanine

FAD

Fig. 3. Typical extrinsic fluorophores used to label macromolecules.

4

In instances where nature has not provided an appropriate fluorophore, one can often add an extrinsic label. The earliest probes include dansyl chloride [l]and ANS (Fig. 3). Dansyl chloride can be covalently attached to macromolecules by reaction with amino groups. ANS often binds spontaneously but non-covalently to proteins and membranes, probably by hydrophobic and electrostatic interactions. The emission of both molecules is sensitive to the polarity of the surrounding environment. ANS is nearly non-fluorescent in water, but fluoresces strongly upon association with serum albumin, immunoglobulins and other proteins. A wide variety of covalent and non-covalent probes are available [2,3]. Studies of cell membranes by fluorescence depends almost exclusively upon the use of extrinsic probes. This is because most lipids are not fluorescent, and the emission from membrane-bound proteins is too heterogeneous for interpretation of the data. The probe DPH (Fig. 3) is typical of membrane probes, as is perylene (Fig. 1).These non-polar molecules partition spontaneously into membranes. And finally, Fig. 3 shows several extrinsic probes for nucleic acids. Addition of the etheno bridge to ATP results in a highly fluorescent residue. Unfortunately, this modification also disrupts the base pairing of the nucleotide. Alternatively, nucleic acids can be labeled by spontaneous binding of planar cations such as ethidium bromide and acridine orange (Fig. 3). Depending upon the structure, the fluorescence of the probe may be quenched or enhanced upon intercalation into DNA, and the emission may depend upon whether the intercalation site is adjacent to A-T or G-C pairs. For instance, the fluorescence yield of ethidium bromide is enhanced about 30-fold upon intercalation into DNA. Other intercalating dyes such as proflavin and 9-aminoacridine are quenched by their interactions with DNA [4].

2. Factors affecting the fluorescence emission 2. I . Solvent polarity and viscosity The variety of factors which can affect the fluorescence emission are illustrated by the modified Jablonski diagram [5] shown in Fig. 4. In this diagram we emphasize fluorescence emission and quenching, and hence we have not included the higher electronic states or the triplet states. Upon absorption of light the fluorophore arrives instantaneously in the first singlet state (Sl), usually with some excess vibrational energy. This excess energy is usually dissipated quickly in lo-'' sec by interaction with the solvent, resulting in a molecule in the lowest vibrational level of S,. The fluorophores remain at this level for the mean duration of the excited state, which is typically 10 nsec. Any process or interaction which occurs during this interval can alter the fluorescence emission. These processes and interactions are the origin of much of the information available from fluorescence spectroscopy. Fluorophores with polar groups are often sensitive to solvent polarity. Interaction between the excited fluorophore and surrounding polar groups lowers the energy of the excited state, which shifts the emission to longer wavelengths. The relative amounts of emission from the relaxed and the unrelaxed states depend upon the

5

\j

S L a R e l a Y Donor Emission

k,

Energy Transfer Acceptor absorption

Xkil

h

a

so

Fig. 4. Jablonski diagram for fluorescence emission and quenching.

relative rates of depopulation of the excited state ( r+ Cki) and that of solvent relaxation ( k R ) .The rate of emission is r and the rate of return to the ground state exclusive of emission is Cki. In fluid solvents near room temperature the rate of solvent reorientation is near 10-1'-10-12 sec. Hence, this process is mostly complete prior to emission, so the observed emission is that of the relaxed state. If the solution is cold or viscous, or if the probe is bound to a rigid site on a macromolecule, then the rates of relaxation and emission can be comparable, so emission is seen from both the relaxed and the unrelaxed states. If the solution is very viscous then solvent relaxation does not occur during the lifetime of the excited state, and the observed emission is from the higher energy (shorter wavelength) unrelaxed state. The effects of solvent polarity are best understood by specific examples. To model the fluorescence emission of proteins we examine spectra for N-acetyl-Ltryptophanamide (NATA). This molecule is analogous to tryptophan in proteins. It is a neutral molecule, and its emission is more homogeneous than that of tryptophan itself. In solvents of increasing polarity the emission spectra shift towards longer wavelengths (Fig. 5). The emission maxima of NATA in dioxane, ethanol and water are 333, 344 and 357, respectively. These solvents are non-viscous, so the emission is dominantly from the relaxed state (Fig. 4). The spectral shifts can be used to calculate the change in dipole moment which occurs upon excitation [6]. More typically, the emission spectrum for a sample is compared with that found for the same fluorophore in various solvents, and the environment judged as polar or non-polar. While this approach is qualitative, it is simple and reliable, and does not involve the use of theoretical models or complex calculations. The timescale of the relaxation process also affects the emission. This effect is illustrated for NATA in propylene glycol (Fig. 6). At room temperature the relaxation is mostly complete, and a red shifted spectrum is observed (348 nm). Lowering the temperature results in a progressive shift of the emission to shorter wavelengths, with an emission maximum of 329 nm at - 60 O C . As the temperature is decreasing the relaxation rate ( k R )becomes slow relative to that of the decay rate ( r+ Cki). Hence, an increasing proportion of the emission is from the unrelaxed and the intermediate states (Fig. 4), which have higher energies and shorter emission

6

WAVELENGTH ,(nanometers)

Fig. 5 . Emission spectra of N-acetyl-L-tryptophanamidein various solvents of different polarities.

wavelengths (Fig. 6). In proteins it is probable that the emission maxima are affected by both the average environment of the tryptophan residues [7] and by the relaxation rates [8]. Rather detailed data and analysis are needed for an unambiguous separation of these effects, but the average environment of the tryptophan residues seems to be the dominant determinant of the emission maxima. 2.2. Emission spectra of melittin Melittin is an amphipathic peptide component of bee venom which associates with cell membranes, enhances the phospholipase activity of venom and participates in the disruption of cell membranes. This protein has been studied extensively by

WAVELENGTH [nanometers)

Fig. 6. Emission spectra of N-acetyl-L-tryptophanamidein propylene glycol at 25 and

- 60

C

WAVELENGTH (nanometers) Fig. 7. Emission spectra of melittin in the absence (data are courtesy of N. Joshi.

) and presence (-

- -)

of 2 M NaCl. The

fluorescence and other physical methods [9,10], and its X-ray structure is known [ll]. In solution melittin exists as either a monomer or a self-associated tetramer. The self-association is driven by high salt concentration, which apparently shields the positive charges on the monomer from each other and allows the hydrophobic interactions to cause association. The monomeric form of melittin is thought to be largely random coil with a high degree of segmental mobility. In the tetrameric state the monomeric units are mostly a-helical. Melittin is an ideal protein to illustrate the effects of structure on the fluorescence spectral properties. Each monomer contains a singly tryptophan residue and no tyrosine residues. The X-ray structure of the tetrameric form shows that the tryptophan residues are buried in a non-polar pocket and are not directly exposed to the aqueous phase. The emission spectra of melittin illustrate the effects of solvent exposure on the tryptophan emission (Fig. 7). In the absence of salt, the emission maximum of 360 nm is comparable to that found for NATA in water. In the presence of 2 M NaCl the emission maximum is blue shifted by 12 nm to 348 nm. This shift is a result of shielding of the indole ring from the aqueous phase. Hence, solvent relaxation proceeds to a lesser extent because there is less solvent available for interaction with the fluorophore. 2.3. Quenching of fluorescence

Collisional quenching of fluorescence requires contact between the fluorophore and the quencher. For quenching to occur the quencher must diffuse to and collide with the fluorophore in the excited state. If this occurs the fluorophore returns to the ground state without emission of a photon (Fig. 4). Many small molecules act as collisional quenchers of fluorescence [6,12]. These include iodide, acrylamide, halogenated hydrocarbons and occasionally amines and metal ions. The excited state lifetimes provide ample opportunity for quenching. For instance, acrylamide is known to be an efficient quencher of tryptophan fluorescence [12,13]. Su.ppose its

8

I P

Melittin 7.01 2 5 O C , p H - 7

Monomer K =

7,2 M-'

k = 2.1x I 0 ' M-'s-'

5.0-

-FF.

0.6

0.4

0.2

0

0.8

[Acrylamidel ,M

Fig. 8. Stern-Volmer plot for acrylamide quenching of melittin monomer and tetramer. From M. Eftink, University of Mississippi, Chemistry Department, unpublished observations. The lifetimes are from [35]. The broken lines are the initial slopes, corresponding to the values on the figure.

diffusion coefficient is lop5cm2/sec. In 10 nsec an acrylamide molecule can diffuse a distance of 44 A, as calculated using A x 2 = 2 0 7 , where A x is the distance, D is the diffusion coefficient and 7 is the fluorescence lifetime. This distance is comparable to the diameter of many proteins. Hence, we expect quenching to occur to a measurable degree and the extent of quenching to be sensitive to the average degree of exposure of the tryptophan to the aqueous phase. Once again melittin illustrates the effect of protein structure on the fluorescence emission. Acrylamide quenching data for melittin monomer and tetramer are shown in Fig. 8. Stern-Volmer plots are often used to present quenchmg data. The Stern-Volmer equation is FO = 1+ k.,[Q]

F

=

1

+K [ Q ]

where Fo and F are the fluorescence intensities in the absence and presence of quenching, respectively, T~ is the fluorescence lifetime in the absence of quenchmg, [ Q ]is the concentration of quencher, k is the bimolecular quenching constant, and K is the Stern-Volmer quenching constant. The lifetime T,, is the reciprocal of the rates which depopulate the excited state. From Fig. 4,

If every collisional event results in quenching, the bimolecular rate constant can be estimated using the diffusion constants of the fluorophore ( D F )and quencher ( DQ) and the radius expected for contact ( R ) , k

(3)

= 4~rRDN/1000

where N is Avogadro's number and D

= D,

+ DQ. If the fluorophore is exposed to

9

the solvent we expect k to be near 0.5 X lo1' M-' sec-'. If the residue is shielded from collisional encounters this rate will be smaller. This comparison is the basis for estimating the extent of exposure from quenching data. The quenching constant measured for a protein is compared with that expected for a completely exposed fluorophore. Typically, model compounds with no possibilities for shielding are studied to account for lack of precise knowledge of diffusion coefficients, and the possibility that the quenching encounter is not 100% efficient. The quenching data for both the monomeric and tetrameric forms of melittin indicate the tryptophan residues are accessible to acrylamide with the accessibility being greater in the monomeric state. This conclusion is reached by comparison with acrylamide quenching data for NATA. At 25°C in water the acrylamide quenching constant for NATA is 0.58 X 10" M-' sec-' [47]. For the monomer the quenching constant is about one-third of this value, which is indicative of a rather fully exposed residue [13]. The value of k for the tetramer is less, indicating shielding of the tryptophan residue from the aqueous phase. It should be noted that the relative shielding is only 40%, which probably indicates considerable penetration of the tetramer by acrylamide. In other more extensive studies Eftink and Ghiron showed that acrylamide quenching reflects the average degree of tryptophan exposure to the aqueous phase [13]. The penetration of proteins by quenchers has been known for some time [14,15]. For melittin tetramer the penetration by acrylamide is not unexpected since acrylamide is neutral and the tryptophans are located in a loosely packed non-polar region of the protein [ll]. 2.4. Fluorescence energy transfer

Another process which can occur during the excited state is fluorescence energy transfer, which is the transfer of the excited state energy from a donor (D) to an acceptor (A) (Fig. 4). The transfer is called radiation-less because it occurs without the appearance of a photon. This process is strongly dependent upon distance because it is the result of dipole-dipole coupling between the donor and the acceptor [16]. A requirement for energy transfer is that the emission spectrum of the donor overlaps with the absorption spectrum of the acceptor. The rate of transfer ( kT) is gven by (4) where R , is the distance at which 50% of the energy is transferred, and r is the donor-to-acceptor distance. The value of R o can be calcuated from the spectral properties of donor and acceptor [6,16]. The efficiency of energy transfer is given by the ratio of the rates of transfer to the total rate of depopulation of the donor. Hence,

10

Usually, both the transfer efficiency ( E ) and R , are determined experimentally. Then, the donor-to-acceptor distance is calculated using

This method is widely used to measure the distance between sites on a macromolecule, and has been the subject of considerable experimentation and discussion [17- 191. Energy transfer has been used to measure the self-association of melittin. The melittin was labeled with a N-methylanthraniloyl (NMA) residue on one of the lysine residues. This fluorophore serves as the energy acceptor for the single tryptophan residue. Only a small fraction (5%) of the melittin monomers was labeled with NMA. In the monomer there is only one tryptophan residue near the acceptor, whereas four such residues are present in the tetramer. Hence, the extent of tryptophan to NMA energy transfer should be sensitive to and increased by melittin self-association. In this experiment the intention is not to determine a distance, but rather to use the association-dependent energy transfer to determine the extent of self-association [20].

300

350

400

450

500

WAVELENGTH (nanometers)

Fig. 9. Emission spectra of N-methylanthraniloyl-labeled melittin. Spectra are shown for the monomer (0 M NaC1) and for the tetramer (2 M NaCI). From [20]. The broken lines are the emission spectra of the unlabeled melittin.

11

250

300

350

400

WAVELENGTH (nanometers 1

Fig. 10. Excitation spectra of NMA-labeled melittin. From [20].

Emission spectra of the labeled melittin are shown in Fig. 9. Recall that only a small fraction of the melittin contains a NMA label. Hence, the emission spectra are mostly characteristic of tryptophan, with shoulders at 430 nm due to the NMA emission. In the presence of 2 M NaCl the NMA emission is enhanced, reflecting increased energy transfer from the additional tryptophan residues. Excitation spectra are often used to study energy transfer. This is because energy transfer can be detected by enhanced emission from the acceptor when the excitation is centered at the donor absorption. The effects of melittin self-association are evident from the excitation spectra (Fig. 10). For these spectra the emission monochromator is centered on the NMA emission (430 nm) and the intensity recorded as the excitation monochromator is scanned through the absorption bands of the NMA label (350 nm) and the tryptophan absorption (280 nm). Increasing salt concentrations result in increased intensity of the tryptophan excitation band (280 nm). This increase in energy transfer is due to the close proximity of the three additional donors to the NMA acceptor.

2.5. Fluorescence anisotropy The timescale of fluorescence emission is comparable to that of rotational diffusion of proteins and the timescale of segmental motions of protein domains or individual amino acid residues. The polarization or anisotropy of the emission provides a measure of these processes. Suppose a sample is excited with vertically polarized light (Fig. ll),and that the sample is viscous so that the fluorophores do not rotate during the lifetime of the excited state. Then the emission is polarized, usually also in the vertical direction. This polarization occurs because the polarized excitation selectively excites those fluorophores in the isotropic solution whose absorption

12

LIGHT

SOURCE-

m+ f/

DETEC~OR Fig. 11. Measurement of fluorescence anisotropies.

moments are aligned vertically. The extent of polarization is most conveniently defined by the anisotropy [6,40].

where I refers to the intensities, and the subscripts indicate the parallel (11) or component. perpendicular (I) A number of processes can result in the loss of anisotropy, the most common being rotational diffusion. Melittin is expected to have rotational correlation times near 2 and 8 nsec in the monomeric and tetrameric states, respectively. The effect of rotational diffusion on the anisotropy is described by the Perrin equation,

where r, is the anisotropy in the absence of rotational diffusion, r is the anisotropy, is the lifetime and 6 is the correlation time. The value of r, is usually measured in a separate low-temperature experiment. Its value depends upon the excitation wavelength, and is typically in the range of 0.1 to 0.4. The r, value is a measure of the angle between the absorption and emission transition moments of the fluorophore. For tryptophan the value of ro on the long wavelength side of the absorption is near 0.32. Values of r, which are less than 0.1 are usually not useful because the difference between 11,and I* will be small, and the precision of the measurements will be decreased. When 7, and 8 are of similar magnitude then the measured anisotropy is dependent upon the correlation time. Self-association of melittin is expected to increase its correlation time about four-fold. Since the lifetime of melittin fluoresence is near 3 nsec we expect self-association to have a dramatic effect on the 7,

13

old0

'

0'4

'

0.8 '

'

I.2 '

'

1'.6

'

2.0 I

'

[NaCII. M

Fig. 12. Fluorescence anisotropies of melittin [20]. Anisotropies are shown both for the intrinsic tryptophan emission (A), and for that of the NMA label (0). Also shown is the effect of salt concentration on the extent of energy transfer (0).

anisotropy. Anisotropy data for melittin at various salt concentrations are shown in Fig. 12. As the salt concentration is increased the anisotropy values increase and reach a plateau whch is characteristic of the tetramer. Also shown in Fig. 12 are the anisotropy values of the NMA label. These also increase with salt concentration, and reach a constant value at 1 M NaC1. The NMA anisotropy values are lower than for tryptophan because the decay time of the NMA label is longer, near 8 nsec. For comparison this figure also shows the extent of energy transfer. All three measurements reflect the monomer to tetramer transition. Anisotropy measurements are generally useful for measuring any process which increases or decreases the rate or extent of rotational diffusion. These processes include domain motions of immunoglobulins [21], denaturation of proteins [22] and the association of proteins with membranes [lo]. Additionally, there are numerous applications of anisotropy measurements to membranes, in which the phase state and apparent fluidity are estimated from the anisotropy of probes which are bound to the membranes [23,24].

3. Time-resolved fluorescence spectroscopy The previous discussion and examples emphasized the use of steady-state fluorescence data. Steady-state data are measured with constant illumination of the sample. The timescale of these measurements is slow relative to the fluorescence decay times. Hence, the effects of the time-dependent processes are averaged to yield the average emission spectra, anisotropies, or extents of energy transfer. Each measured steady-state quantity is the average of the time-dependent values of that quantity averaged over the time-dependent decay of the sample. For instance, the

14

steady-state anisotropy is determined by its time-resolved decay ( r (t )) and the time-dependent decay of the emission ( Z ( t ) )

If we assume that both r ( t ) and I ( t ) decay as single exponentials with time constants of 1/8 and 1/~,,, respectively, then application of equation 9 yields the steady-state form, whch is the Perrin equation (8). At present, there is widespread interest in directly measuring the time-dependent processes. This is because considerably more information is available from the time-dependent data. For example, the time-dependent decays of protein fluorescence can occasionally be used to recover the emission spectra of individual tryptophan residues in a protein. The time-resolved anisotropies can reveal the shape of the protein and/or the extent of residue mobility within the protein. The time-resolved energy transfer can reveal not only the distance between the donor and acceptor, but also the distribution of these distances. The acquisition of such detailed information requires high resolution instrumentation and careful data acquisition and analysis. There are presently two methods of obtaining the time-resolved data. These are by direct measurements in the time-domain [25,26] and by less direct measurements

TIME

I

0

TIME

I

20

1

I

40

I

1

60

TIME (nanoseconds)

Fig. 13. Measurement of time-resolved fluorescence in the time-domain (top) and in the frequency-domain (bottom).

15

in the frequency-domain [27,28]. For time-domain measurements the sample is excited with a brief pulse of light (Fig. 13). The time-dependent fluorescence intensities are used to estimate the decay time(s) of the sample. In the frequency-domain the sample is excited with intensity modulated light. The frequency response (phase and modulation) of the sample are used to estimate the decay time(s). Both methods are rapidly evolving to take advantage of the increased time resolution obtainable using picosecond pulse lasers and faster detectors [29,30]. The complex equipment and analyses necessary for time-resolved measurements has been the subject of numerous publications and monographs [25,26]. In this article we will not describe the instrumentation, but will rather describe the results and their interpretation. The objective of either time or frequency-domain fluorometry is to determine the decay law of the sample. For example, consider protein containing two tryptophan residues, and assume further that each residue has a single decay time. The impulse response of the sample is the decay which would be observed with an ideal instrument following excitation with a &function light pulse. For our hypothetical protein we expect a doubly exponential decay of intensity, 2

I( t ) =

C aie-'/'~ i=l

In this expression the 7; values are the decay times of the individual residues and ai values are the preexponential factors. The contribution of each residue to the emission is

Suppose the data are measured at a number of wavelengths across the emission spectrum. Then the data are described by 2

I(X, t)=

C a,(X)e-f'Ti i=l

where X indicates the emission wavelength. Under favorable conditions, such data allow the spectrum of each residue to be recovered. This can be seen by recognizing that the values of h(X) represent the fraction of the total emission due to each residue. This illustrates how the time-resolved data provide information not obtainable from the steady-state spectra. 3.1. Resolution of the emission spectrum of liver alcohol dehydrogenase

The resolution and understanding of the emission from proteins is a difficult task. This is because most proteins contain two or more tryptophan residues, and even

16

10'

10'

b double

I oJ

I oJ

in

in

tZ

t-

z

:

3

u

u

3

;I 0 2

102

0

0

1

_I

10'

10'

1

100

0

1

1

1

I

100

200

300

400

I oo

i

100

0

500

200

30C

400

500

400

500

CHAFJNELS

CHANNELS

aooo

aooo

6000

I'

A

'I

6000

m

! I

54 0 0 0

5400C

t-

+

0

0

u

0

200[

2000

in0

200

300

400

so0

CHANNELS

0

100

200

300

CHANNELS

Fig. 14. Time-resolved fluorescence intensity of liver alcohol dehydrogenase. Left: single exponential fit, x i = 1.14. The faster decaying curves are the lamp profiles found using scattered light. The upper panels are on a semilogarithmic scale, and the lower are on a linear scale. The lower panels show the deviations, and the autocorrelation of the deviations as insets.

x i = 3.02; right: double exponential fit,

the emission from proteins containing a single tryptophan is complex or multi-exponential. One of the most detailed studies is for liver alcohol dehydrogenase (LADH) by Brand and co-workers [7]. LADH consists of two identical subunits (dimeric) with a molecular weight of 80,000 daltons. Each subunit contains two tryptophan residues, trp-15 and trp-314. One residue (trp-15) is exposed to the solvent, while t h s other (trp-314) is in a hydrophobic pocket at the dimer interface. Time-resolved data for LADH are shown in Fig. 14. These data for a single emission wavelength, were obtained by the method of time-correlated single photon

17

counting [25,26]. The light source is a flash lamp which fires repetitively at rates near 20 kHz. The time-resolved decay is obtained by measuring the time interval between the lamp pulse and the first emitted photon. The rate of detecting the emitted photons is kept near 2% of the lamp rate. In this way the first photon represents a sampling of the entire time-resolved decay. If many photons reach the detector, and only the first one is counted, then the measured decay does not represent the true decay. The electronic circuits (in current use) which detect the arriving photons cannot accept and process multi-photon events, which limits the rate of data acquisition. A second difficulty is the width of the lamp pulse. Flash lamps are inexpensive, but the pulse widths are near 2 nsec, whch is not much shorter than the decay times of proteins. Consequently, mathematical procedures, known as deconvolution or reconvolution, are used to account for the lamp pulse width. Nonetheless, the necessary procedures are highly refined and reliable. The data for LADH (Fig. 14) illustrate how the time-resolved data are analyzed. The analysis starts by assuming the decay is a single exponential (equation 1 with i = l),and calculation of the best fit. This fitting procedure involved use of the lamp profile and a guess of the decay time to predict the data. The numerical value of the single decay time is varied until the best fit is found. Frequently, a single decay time model is not adequate, as was found for LADH. The inadequacy of the fit is revealed by systematic deviations between the measured and calculated data (Fig. 14, lower left), and an unacceptably high value for the goodness-of-fit parameter xi = 3.02. For an acceptable fit xi should be near unity. Greater values of xi can be the result of either an inadequate model or systematic errors in the data. The acceptable values of xi are determined, in principle, by statistical criteria [41], but individual judgements are necessary. The next step in the analysis is to fit the data using a more complex model. The best fit for LADH for two decay times yields an improved match (Fig. 14, right). The calculated and measured values are now in agreement, the deviations are small and random, and xi = 1.14 is acceptably close to unity. The parameters (a,and 7,) which yield this match are taken as the decay law of the sample. The decay times (3.8 and 7.2 nsec) were taken to be due to tryptophan 314 and 15, respectively. It must be emphasized that this result does not prove the decay is a double exponential, but only shows that the double exponential model is adequate to explain the data. If data were available with higher time resolution or statistical accuracy (more photons) then it may be necessary to use a more complex three-exponential decay model to explain the data. To resolve the emission spectra of each residue similar data were collected at closely spaced wavelengths across the emission. The assumption was made that the decay time of each tryptophan residue was independent of emission wavelength, and constant across the emission. The measured decay law was used to calculate the individual spectra using

18 I

I

I

1

m

F 5

w

LL4

T, = 3 8 0 n s T2 = 7.22 ns

3 2 0 3 5 0 380

410

WAVELENGTH (nm)

0 WAVELENGTH

(NMi

Fig. 15. Lifetimes, amplitudes and emission spectra of the two tryptophan residues in liver alcohol dehydrogenase 171.

These spectra are shown in Fig. 15. The shorter-lived trp-314 (3.8 nsec) showed a shorter-wavelength emission, whereas the longer-lived trp-15 emitted at longer wavelengths. Hence, the emission spectrum and decay time of each tryptophan residue in LADH were resolved. 3.2. Pulsed lasers for time-resolved fluorescence

The time-resolved emission of LADH was found to be complex due to the presence of two tryptophans. It is highly probable that the results in Fig. 15 are only approximate, and that the decay of each tryptophan is multi-exponential. Such complexity is hidden from view by the limited resolution of the available instrumentation. The resolution of more complex decays for LADH or any protein requires higher resolution. This is being accomplished by the use of pulsed laser sources. One of the most popular sources is shown in Fig. 16. The main pump is shown as an Ar-ion laser, but the Nd-YAG lasers are used in a similar manner. Normally, these lasers yield continuous output. In this case the argon laser is mode-locked, which yields a repetitive train of pulses. These pulses are spaced at the time interval for light to travel the length of the laser cavity, which is 83 MHz. The argon laser output is then used to pump a dye laser, whose cavity length is identical to that of the Argon laser. This results in a 83 MHz train of pulses in the dye laser cavity which has pulse widths near 5 psec. These pulses are extracted at a slower rate using a cavity dumper. The cavity dumper is a small piece of quartz into which a time R F pulse is launched via a piezoelectric device. This RF pulse sets up a diffraction grating which deflects the desired laser pulse. The extracted pulse train is then

19

514nm

I

1

n

I

I

U

1

570-610 nm

u

0.1 (0 4 MHz

u 83 MHz

I

I

I

D Y E LASER

CAVITY D U M P E R

-

285 305 nm DOUBLER

5ps 4MHz

Fourier Transform

-

b 0

a

Time Frequency (GHz)

Fig. 16. Pulsed laser source for time-resolved fluorescence. The lower panel shows the pulse train from the laser source and its Fourier transform.

frequency-doubled to yield the UV necessary to excite protein fluorescence. Additional details are available in other books on this topic [42,43]. There are several significant advantages to the laser source over the more conventional flash lamp. The laser source is more intense. Its pulse width is near 5 psec, as compared for 2000 psec for a flash lamp. And finally, the repetition rate can be much higher, typically 800 kHz to 4 MHz. Because of all these factors it is possible to rapidly acquire data to a much higher level of statistical accuracy than with a flash lamp. For example, a recent paper by Small and co-workers describes a multi-component resolution of a histone, which contains a single tyrosine residue [31]. Because of the substantial increases in resolution, the laser sources are becoming more widely used in the biochemical applications of fluorescence, as illustrated by recent studies of the tryptophan emission from phospholipase A, [44] and hemoglobin [45]. 3.3. Frequency-domain resolution of protein fluorescence

Multi-exponential decays of fluorescence can also be recovered by measurements in the frequency-domain. This has only become practical within the past four years [27,28]. The resolution of multi-exponential decays requires measurements over a wide range of light modulation frequencies. Earlier instrumentation could operate at only one to three frequencies, and these limited data were not adequate to determine the four parameters in equation 10 (two a, and two T,). The new instruments

20

2.57

1.0

0.15

0.04

5.52

0.33

2 1 ~ 5 l O l

(I. 25

! 2

5

1.03

10

20

50

100

200

FREQUENCY (MHz) Fig. 17. Frequency-domain data for the intrinsic fluorescence of S, Nuclease and melittin.

operate over a wide range, typically 1 to 200 MHz, and some instruments now operate to 2000 MHz [37]. Typical frequency-domain data for two proteins are shown in Fig. 17. The data consist of the phase angles and modulation, each measured over the widest possible range of frequencies. This requirement illustrates the transform relationship between the time and the frequency-domain measurements. In the time-domain, the most desirable excitation profile is the shortest obtainable pulse. The Fourier transform of a &function consists of all frequencies. Hence, the experimental requirements are similar, short pulses or wide range frequencies. For each protein (Fig. 17) the phase angle increases and the modulation decreases as the frequency increases. The data are analyzed in a manner analogous to the time-domain data. That is, a decay law is assumed and the parameters varied until the best possible match is obtained - - -) values. The adequacy of between the measured (0)and calculated (-, the fit is judged by the value of the xi, which is a weighted sum of the squared deviations between the measured and the calculated values. If the value of is significantly larger than unity then the model can be rejected. Both melittin and S, Nuclease contain a single tryptophan residue. The data illustrated the point that the emission from such simple proteins can be multiexponential. Even though only a single residue is responsible for the emission, it was not possible to fit the data using a single decay time. This is shown by the failure of the single decay time model (- - -) to explain the data. The decays are referred to as being heterogeneous. The decays of both nuclease and melittin are signifi-

xi

21

cantly heterogeneous. The decay of melittin is more heterogeneous as seen by the greater deviations of the data from the one decay time model, and the larger value of xk. For both proteins the data can be explained by more complex decay laws. Two decay times are needed to fit the data for nuclease, and three are needed for melittin. It is important to exercise clear thinking when fluorescence data in either domain are fitted to various models. A poor fit can be used to reject a model. The poor fit can be due to either an inadequate model or due to systematic errors in the data not known to the researcher. If systematic errors occur a more complex model could be accepted to account for the errors, not because the model is appropriate for the sample. Secondly, a good fit does not prove the model which yields the good fit is correct. A good fit only shows that the model is adequate to explain the data. Alternatively stated, the data which yield the good fit are not adequate to support a more complex model. What is the origin of the multi-exponential decays found for single tryptophan proteins? Surprisingly, this is an unanswered question which is the focus of current research. Clearly, the protein matrix provides a unique but asymmetric environment for each tryptophan residue. The spectral properties (emission maximum, lifetimes, anisotropy and yield) are determined by this environment. The protein environments can now be conveniently examined using the X-ray coordinates and modem computer graphics, Additionally, it is becoming increasingly easy to replace individual amino acid residues using the techniques of molecular biology. These capabilities, and the increased resolution available from state-of-the-art instrumentation, should allow the linkage to be established between structural data and fluorescence spectral parameters. 3.4. Anisotropy decays of protein fluorescence

There is considerable interest in measuring the rotational diffusion and the dynamic properties of proteins. The rates of rotation diffusion can reveal the size and shape of the protein. Also, proteins are known to undergo structural fluctuations, a topic which has been broadly studied by both experimentation and computer simulations [32-361. The time-resolved experiments are often directed towards a comparison of the measurable dynamics of proteins with the calculated dynamics. One promising approach is to use anisotropy data from intrinsic protein fluorescence. If such data are available with picosecond resolution then such a comparison should be possible. In the time-domain the anisotropy decay is obtained from the time-resolved decays of the parallel and perpendicular polarized components of the emission. More specifically, one measures the time-resolved decays of the parallel ( II) and the perpendicular ( I) components of the emission, and calculates the time-resolved anisotrop y,

22

Generally, the anisotropy decay is multi-exponential

In this expression r( t ) is the time-dependent anisotropy, Bi the correlation times and g, the fraction of the total anisotropy ( r o )whch decays with this correlation time. In general we expect one component (8,) due to rotational diffusion of the protein, and one due to torsional motions of the tryptophan residue, if such motions are significant. In proteins which contain more than a single fluorescent residue there can be energy transfer among the residues, whch can appear as a component in the anisotropy decay. The timescale of energy transfer depends upon the distance and orientation between the residues, but there is little information on the timescale of energy transfer between intrinsic fluorophores in proteins. The measurements are different in the frequency-domain. In this case we measure the phase shift between the parallel and perpendicular components of the emission, and a frequency-dependent anisotropy, which is analogous to the steady state anisotropy. These two types of data are used to determine the decay law for the anisotropy (equation 15). Melittin and S, Nuclease illustrate how the anisotropy decay is reflected in the frequency-domain data. From earlier studies it was known that the single tryptophan residue in S, Nuclease was mostly rigid [36], so that its anisotropy decay should display a single correlation time for rotational diffusion near 11 nsec. In contrast, melittin monomer is thought to be disordered in aqueous solution, so that a rapid anisotropy decay is expected due to local tryptophan motions. The frequency-domain anisotropy data for nuclease and melittin are shown in Fig. 18. The data for nuclease are nearly Lorentzian and centered near 30 MHz, which is expected for a single correlation time near 11 nsec. In contrast, the differential phase data for melittin show no such maximum, and the phase angles increase up to the 200 MHz limit. This is characteristic of a subnanosecond anisotropy decay. For both proteins a multi-exponential anisotropy decay was necessary to explain the data, and in both cases a short correlation time ( < 1 nsec) was indicated by the data. In the case of nuclease only 12% of the anisotropy decays by this rapid process, indicating that the torsional motions have a limited amplitude. In contrast, 75% of the melittin anisotropy decays by the rapid process, which indicates considerable free motion of the tryptophan residue. To illustrate the nature of the anisotropy decays the equivalent time-dependent anisotropies are shown as an insert. These were calculated from the frequency-domain data. For S, Nuclease the plot of log r ( t ) versus time is mostly linear with a slope of (12 nsec)-'. This is the portion of the anisotropy decay due to overall rotational diffusion of the protein. The rapid component in the nuclease anisotropy decay is seen only near the t = 0 origin. The anisotropy decay of melittin is much more rapid, which reflects the greater motional freedom of the tryptophan residue in this disordered polypeptide. Because of the segmental motions which depolarize the

23

O

2

5

10

20

FREQUENCY

50

100

200 f

(MHz)

Fig. 18. Frequency-domain resolution of the anisotropy decay of S, Nuclease and melittin monomer. Melittin: r( t ) = 0.24 exp (- t/0.26) + 0.08 exp (- r/3.04). Nuclease: r( t ) = 0.04 exp (- r/0.20) + 0.28 exp ( - r/12.18).

emission the rotational diffusion of melittin is barely evident in the anisotropy decay.

4. Harmonic-content frequency -domain j7uorometry The frequency-domain data for melittin (Fig. 18) revealed the need for still higher modulation frequencies. Resolution of the anisotropy decay parameters is decreased if the phase angle maximum is not reached. This is perhaps analogous to the data obtained with flash lamps (Fig. 14), in which the width of the pulse was comparable to the decay times of the emission. Very recently, this laboratory developed a hybrid instrument which uses components typical of both time-domain and frequency-domain fluorometers [37]. The instrument uses a 4 MHz train of 5 psec pulses from a cavity-dumped dye laser, whch is the same source as is used for time-correlated single photon counting (Fig. 16). However, the pulses are not used to perform time-domain measurements. The pulse train possesses intrinsic modulation to many GHz, which is shown by the Fourier transform in Fig. 16. This source can be used directly as the modulated light source, an idea proposed originally for pulsed laser excitation by Merkelo et al. [46] and expanded to use the higher harmonics of pulsed synchrotron radiation by Gratton and Degado [48,49]. When used with a fast detector the frequency-domain measurements now extend to 2 GHz [37].

24

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.. .. ....... ._.-.-a_..

.

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. .. .,

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... . ... ..

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FREQUENCY (MHz) Fig. 19. Frequency-domain intensity decay of oxytocin at 20 O C. The symbols (0)represent the data, the solid line the best three-exponential fit, and the dashed line the best one-exponential fit. The lower panels show the deviations between the data and the calculated values for the one (A) and three (0) decay time models. The values of xk are 377, 5.9 and 2.1 for the 1, 2 and 3 exponential fits, respectively.

6

I

0

/'

I

20

I 1 1 1 1 1 1

50

100

I

200

I

I

I

I I , , ,

500

I

1000 20'0

FREQUENCY (MHz) Fig. 20. Anisotropy decay of oxytocin tyrosine fluorescence. The data (0) could not be fitted using a ). The single correlation time (- - -), but were adequately fitted using two correlation times (values of x i are 292, 3.3 and 3.4 for the 1, 2 and 3 correlation time fits, respectively.

25

This development is recent, and harmonic-content data are not yet available for the proteins described above. However, the potential of the 2 GHz measurements is illustrated by the data for oxytocin, which is a cyclic nona-peptide containing a single tyrosine residue. The frequency-response for the intensity decay is shown in Fig. 19. The mean decay time for oxytocin is near 0.7 nsec. Even with this short decay time the entire frequency response was measured, as seen by phase angles which extend to 70" and modulations which decrease to 20%. These data are adequate to support a three exponential analysis. The apparent decay times are 80, 359 and 927 psec. Once again, we find that even the decay of a single tyrosine residue can be complex. The 2 GHz data provide resolution of complex anisotropy decays on the picosecond timescale. Data for the anisotropy decay of oxytocin are shown in Fig. 20. It was not possible to fit the data using a single correlation time (- - -, xi = 292). In contrast, a two-correlation time model provides a good fit, which is not improved by the use of a third correlation time. We believe the correlation times of 29 and 454 psec reflect local tyrosyl motions and overall rotational diffusion, respectively. It is important to note that the measurements to 2 GHz provide considerable information beyond the data to the previous 200 MHz limit. Data to 200 MHz would not display the shoulder seen at 600 MHz, which represents the transition from rotational diffusion to segmental motions.

5. Summary The phenomenon of fluorescence can provide information about the physical properties of proteins and other macromolecules. The information content results from the sensitivity of the spectral properties to the average and dynamic properties of the environment surrounding the fluorescent residues. In general, more detailed information is obtainable from time-resolved data than from steady-state measurements. However, the steady-state measurements are considerably easier to perform. At present, the ability to recover time-resolved spectral data is rapidly improving, primarily because of advances in instrument design. The newer instruments may possess resolution adequate to correlate experimental data with the structural or dynamic properties of macromolecules.

Acknowledgements This work was supported by grant DAAG29-85-G-0017 from the Army Research Office, grants DMB-8511065 and DMB-08502835 from the National Science Foundation and grants GM-39617 and GM-29318 from the National Institutes of Health. The author wishes to especially acknowledge the National Science Foundation for providing support to construct the frequency-domain fluorometer, at a time when there were doubts about their design and usefulness.

26

References 1 Weber, G. (1952) Biochem. J. 51, 155-167. 2 Haugland, R.P. (1983) In: Excited States of Biopolymers (R.F. Steiner, ed.) pp. 29-58, Plenum Press, New York. 3 Beddard, G.S. and M.R. West, eds. (1981) Fluorescent Probes. Academic Press, New York. 4 Steiner, R.F. and Y. Kubota (1983) In: Excited States of Biopolymers (R.F. Steiner, ed.) Plenum Press, New York. 5 Jablonski, A. (1935) Z. Phys. 94, 38-46. 6 Lakowicz, J.R. (1983) Principles of Fluorescence Spectroscopy. Plenum Press, New York. 7 Ross, J.A.B., C.J. Schmidt and L. Brand (1981) Biochemistry 20, 4369-4377. 8 Lakowicz, J.R. and H. Cherek (1980) J. Biol. Chem. 255, 831-834. 9 Talbot, J.C., J. Dufourcq, J. DeBong, J.F. Faucon and C. Lussan (1979) FEBS Lett. 102, 191-193. 10 Faucon, J.F., J. Dufourcq and C. Lussan (1979) FEBS Lett. 102, 187-190. 11 Terwillinger, T.C. and D. Eisenberg (1982) J. Biol. Chem. 257, 6016-6022. 12 Eftink, M.R. and C.A. Ghiron (1981) Anal. Biochem. 144, 199-227. 13 Eftink, M.R. and C.A. Ghiron (1976) Biochemistry 15,672-680. 14 Lakowicz, J.R. and G. Weber (1973) Biochemistry 12,4161-4170. 15 Lakowicz, J.R. and G. Weber (1973) Biochemistry 12, 4171-4179. 16 Forster, Th. (1948) Ann. Phys. (Leipzig) 2, 55-77. Translated by R.S. Knox. 17 Stryer, L. (1978) Annu. Rev. Biochem. 47, 819-846. 18 Stryer, L. and R.P. Haugland (1967) Proc. Natl. Acad. Sci. USA 58, 719-726. 19 Dale, R.E., J. Eisinger and W.E. Blumberg (1979) Biophys. J. 26, 161-194. 20 Hermetter, A. and J.R. Lakowicz (1986) J. Biol. Chem. 261, 8243-8248. 21 Hanson, D.C., Y. Yguerabide and V.N. Schumaker (1981) Biochemistry 20, 6842-6852. 22 Brand, J.C. and R.H. Cagen (1977) Biochim. Biophys. Acta 497, 178-187. 23 Dale, R.E., L.A. Chen and L. Brand (1977) J. Biol. Chem. 252, 2163-2169. 24 Kawato, S., K. Kinosita and A. Ikegami (1977) Biochemistry 16, 2319-2324. 25 OConnor, D.V. and D. Phillips (1984) Time-Correlated Single Photon Counting. Academic Press, New York. 26 Demas, J.N. (1983) Excited State Lifetime Measurements. Academic Press, New York. 27 Lakowicz, J.R. and B.P. Maliwal (1985) Biophys. Chem. 21, 61-78. 28 Gratton, E. and M. Limkemann (1983) Biophys. J. 44, 315-324. 29 Visser, A.J.W.G., ed. (1985) Anal. Instrum. 14, 193-566. 30 Lakowicz, J.R., G. Laczko and I. Gryczynski (1986) Rev. Sci. Instrum. 57, 2499-2506. 31 Libertini, L.J. and E.W. Small (1985) Biophys. J. 47, 765-772. 32 Gurd, F.G. and T.M. Rothgeb (1979) Adv. Prot. Chem. 33, 73-165. 33. Karplus, M. and J.A. McCammon (1981) CRC Crit. Rev. Biochem. 9, 243-249. 34 Lakowicz, J.R. (1986) Methods in Enzymology, in press. 35 Lakowicz, J.R., G. Laczko, I. Gryczynski and H. Cherek (1986) J. Biol. Chem. 261, 2240-2245. 36 Munro, I., I. Pecht and L. Stryer (1979) Proc. Natl. Acad. Sci. USA 76, 56-60. 37 Lakowicz, J.R., G. Laczko and I. Gryczynski (1986) Rev. Sci. Instrum. 57, 2499-2506. 38 Lakowicz, J.R., G. Laczko and I. Gryczynski (1986) Biophys. Chem. 24, 97-100. 39 Lakowicz, J.R. and Balter, A. (1982) Photochem. Photobiol. 36, 125-132. 40 Jablonski, A. (1960) Bull. Acad. Pol. Sci. 8, 259-264. 41 Bevington, P.R. (1969) Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New York. 42 Svelto, 0. (1982) Principles of Lasers. Plenum Press, New York. 43 Visser, A.J.W.G., ed. (1985) Analytical Instrumentation 14. Marcell Dekker, New York. 44 Ludescher, R.D., Volwek, J.R., DeHaas, G.H. and Hudson, B.S. (1985) Biochemistry 24, 7240-7249. 45 Albana, J., Albert, B., Krajcarski, D.T. and Szabo, A.G. (1985) FEBS Lett. 182, 302-304. 46 Merkelo, H., Hartman, S.R., Mar, T., Singhal, G.S. and Govindjie (1969) Science 164, 301-302. 47 Eftink, M. and Ghiron, C.A. (1976) J. Phys. Chem. 80, 486-493. 48 Gratton, E. and Degado, L.R. (1980) Nuovo Cimento 56, 1110-1124. 49 Gratton, E. and Delgado, L.R. (1979) Rev. Sci. Instrum. 50, 789-790.

A. Neuberger and L.L.M. Van Deenen (Eds.) Modern Physical Methoak in Biochemistry, Part B 0

27

1988 Elsevier Science Publishers B.V. (Biomedical Division)

CHAPTER 2

Raman and resonance Raman spectroscopy * P.R. CAREY Division of Biological Sciences, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR6

1. Introduction When a beam of monochromatic light is incident on, for example, a liquid a small portion of the light undergoes a change in wavelength. That portion which changes wavelength is known as the Raman spectrum after the Indian scientist C.V. Raman who with his colleague K.S. Krishnan first reported the effect [l].In the biochemical context Raman spectroscopy is used principally to monitor the vibrational motions of atoms within a molecule. Since the vibrational spectrum is sensitive to the molecule’s conformation and environment the Raman spectrum is used to probe the detailed chemistry of the biochemical molecule under study [2-41. The physical origin of Raman scattering lies in inelastic collisions between the molecules composing the liquid and photons which are the particles of light making up the light beam. An inelastic collision means that there is an exchange of energy between the photon and the molecule with a consequent change in energy, and hence wavelength, of the photon (Fig. 1). Moreover, since total energy is conserved during the scattering process the energy gained or lost by the photon must equal an energy change within the molecule. It follows that by measuring the energy gained or lost by the photon we can probe changes in molecular energy. The changes in the molecule’s energy are called transitions between molecular energy levels. As already mentioned, in biochemical studies Raman spectroscopy is concerned primarily with the molecule’s vibrational energy level transitions although the resonance Raman effect also provides detailed information on electronic energy levels. Although present-day Raman spectroscopy uses high technology-based instrumentation the experimental technique is simple in conception and can usually be depicted as in Fig. 2. A monochromatic laser beam of wavelength, A, is focussed into the sample to produce a high photon density and the resulting scattered light, which includes the Raman spectrum, is analysed for wavelength and intensity. The Raman effect is extremely weak and only a minute proportion of the incident * Published as NRCC Number 28, 789.

28

Molecule w

incident photon wavelength A, Scattered photon wavelength A,

For Raman scattering

A,

A,

Fig. 1. An inelastic collision between a photon and a molecule. From [2].

photons become Raman photons of wavelengths A,, A,, etc. The inherent weakness of the effect means that relatively high-power lasers must be used to create a high photon flux and that sophisticated optical and electronic equipment is required to detect the scattered photons. The normal Raman scattering process is improbable and gives rise to a weak Raman spectrum. However, there is a condition under which the spectrum can be greatly intensified, as a result of a phenomenon known as the resonance Raman (RR) effect. The Raman spectrum, obtained using an excitation wavelength of 488 nm, of the dithioester methyl dithioacetate is illustrated in Fig. 3. The spectrum has peaks whch contain contributions from the stretching motions of the C-H, C = S respectively. This Raman spectrum, although and C-S bonds, vC-H, vC+ and easily recorded using modern equipment, is extremely weak. However, under the resonance condition considerable intensity enhancement can occur. This condition is also illustrated in Fig. 3; the dithioester group has an intense electronic absorption transition near 302 nm and using an excitation wavelength (e.g. 324 nm) that lies under the absorption band a marked increase in Raman scattering is observed. Peaks occur in the same positions (usually denoted on a cm-' scale as in infrared spectroscopy) in both the Raman and the RR spectra, but only peaks which are

-

/ scattered light analysed forwavelength,

sample

_C

A, A2A3etc, and intensity

\ \ collecting lens focussing lens

laser beam wavelength A ,

Fig. 2. Schematic of a Raman experiment. From [2].

29

t S

H,C-C,

4

S-CH,

Resonance Ramon spectrum

1

f w=s "C-H "c-s FExciting line 488 nrn I

;

1

300

I

400

I

I

500 NANOMETERS

c

Fig. 3. The main features in the absorption, resonance Raman and normal Raman spectra of methyldithioacetate showing their relative positions on the wavelength scale. The choice of the 488 nm exciting line is arbitrary since any wavelength longer than 400 nm would yield a normal Raman spectrum. From

PI. intimately connected with the electronic absorption process are more intense under resonance conditions. For example, in the Raman spectrum shown in Fig. 3 three features are evident; however, in the RR spectrum it appears that only two remain. This is because the v,--~ and v , - = ~features are associated with the electronic transition at 302 nm and are thus intensity enhanced by approximately 2000-fold compared to the normal Raman case. However, the C-H bonds are not associated with the electronic transition and the v , - - ~feature is not intensity enhanced. This results in the relatively weak v ~ being - ~'lost' in the background noise of the RR spectrum. A major advantage of Raman spectroscopy for the analysis of biomolecules stems from the fact that water has a weak Raman spectrum. This enables us to record spectra of aqueous solutes at 10-'-10-2 M with little interference from the solvent. For a chromophore under the RR condition the concentration range becomes 10-4-10-6 M. Moreover, the intensity enhancement associated with the RR effect confers the important advantage of selectivity, allowing one to observe selectively the vibrational spectrum of a chromophore which is just one component of an extremely complex biological system. Other advantages are that Raman and RR spectra can be recorded using small amounts of material (e.g. 10 pl of a liquid) and that most materials such as liquids, gases, fibers and crystals are amenable to analysis.

2. The units used in Raman spectroscopy The units employed in Raman spectroscopy can best be explained by reference to an example. The Raman spectrum of water, the biological solvent, is shown in Fig.

30

,

I

500

NANOMETERS

525

550

575

600

> k

m

z + W

2

I

1

I

RAMAN SHIFT (cm-1)

a00

I9500

18500

I7500

I6500

ABSOLUTE (cm-1)

Fig. 4. A Raman spectrum of water.

4. The spectrum was obtained in the manner illustrated in Fig. 2 using a laser beam

of wavelength 488 nm. The most readily discernable peaks are the intense feature marked 0-H stretch and the weak feature marked H-0-H bend. These Raman peaks arise, respectively, from an exchange of energy between the incoming photons and a vibrational motion corresponding to a stretching of the 0-H bond or a bending motion of the water molecule.

In Fig. 4 the abscissa represents an energy difference between the scattered and incoming photons with the zero point energy difference being at the wavelength of excitation, marked 488 nm. It is therefore apparent that more energy is required to bring about the 0-H stretching motion than the H-0-H bending motion. It is also apparent from the intensities of the peaks in the spectrum that the exchange of energy between molecules and photons giving rise to the 0-H stretching peak is more probable than that giving rise to the H-0-H bending feature. A monochromatic light beam is characterised by its wavelength, A, its power and its polarisation. Instead of quoting the wavelength of a light beam this property is often given in terms of the equivalent units of frequency or wavenumber. These quantities are related to wavelength thus: Frequency = v

C

=

- Hertz (or cycles per second)

h

(1)

31

where c is the speed of light (2.998 X 10" cm sec-' in vacuum) and A must be expressed in the same units as c. 1 Wavenumber (often denoted w or u) = - cm-'

A

(2)

where A is expressed in centimeters. The wavelength of light is commonly expressed in Angstroms (A) or nanometers (nm) 10 A = 1 nm = 1 0 - ~meter

(3)

Finally, the wavelength of light is related to the energy, E , by using E=hv

(4)

where h is Planck's constant. The units described in Fig. 4 are now clear. The wavelength of the laser line used to excite the Raman spectrum is 488 nm which is equivalent to 20,492 cm-'. When discussing energies it is simpler to use wavenumbers since, from equation (4), energy is linear with wavenumber (and therefore proportional to 1/ wavelength). The exchange of energy between the incoming photons and the vibrational energy transitions giving rise to the H-0-H bending and 0 - H stretching features results in a loss in energy for the photons equivalent to 1640 and 3400 cm-', respectively. Thus, on the scale of absolute cm-' the H-0-H bending and 0-H stretch appear at 20,492-1640 = 18,852 cm-' and 20,492-3400 = 17,092 cm-', respectively, and this can be seen by referring to the bottom scale in Fig. 4. The usual convention in Raman spectroscopy is to quote the positions of the vibrational peaks as the difference between the absolute wavenumbers of the exciting line and the absolute wavenumbers of the scattered photon. Thus, the Raman shift scale seen in Fig. 4 is normally the only scale encountered in published Raman spectra. The equivalent wavelength scale in nanometers is shown at the top of Fig. 4 and the nonlinearity of the top scale reflects the fact that spectrum is plotted as a linear function of energy but that energy is proportional to the reciprocal of wavelength.

3. A model for Raman scattering based on classical physics A light wave is a travelling wave of electric and magnetic fields, of which only the electric component gives rise to Raman scattering. When a light wave meets a molecule consisting of electrons and nuclei the electric field will exert the same force on all electrons in the molecule and will tend to displace them from their average positions around the positively charged nuclei. Crucially, for the Raman process the displacements result in an induced dipole moment B in the molecule which is, to a good approximation, proportional to the electric field strength E . Thus Ir=(YE

(5)

32

where the proportionality factor a is called the electric polarisability of the molecule. In general the vector IT will have a different direction from that of the vector E , and therefore a is not a simple scalar quantity. In fact, a is a tensor but in the following simplified treatment we will be dealing with the relationship between just one component of the tensor, a,, and the components of IT and E in the z direction. The electric field of the light wave varies with time. If a fixed molecule is irradiated with monochromatic radiation of frequency vo, expressed in Hertz, which is plane polarised in the z direction, E, as a function of time is given by E , ( t ) = E m , cos 2.rrvot

(6)

where Em, is the value of E, at its maximum and f is the time in seconds from an arbitrary starting time. Thus, for the z component of IT .rr,(t) = aZZEm,cos 27rv0t

(7)

Since .rr, depends on a,= as well as E, the properties of the molecule can change In the present context a varies with time as a consequence of the vibrations of the molecule, since the ease with which electrons may be displaced by the electric field depends on how tightly they are bound to the nuclei, which in turn depends on the internuclear separation. The result of the time dependence of a and E on IT can be seen by considering the simple example of a single diatomic molecule. For a diatomic molecule the difference from equilibrium in the internuclear distance at time t , Ar(t) can be written rZvia a.

Ar( t ) = Arm,(2.rrv,,t

+ cp)

(8)

where vVib is the vibrational frequency of the molecule in Hertz, and Arm, is the maximum extension of the distance between the two atoms. By taking the time t to have the same starting point as the time scale for the light wave in equation (6), the phase constant cp may be equated to zero. Using the postulate that the polarisability of the diatomic molecule depends linearly on Ar, the azzcomponent of a can be written: a,,(t) =

dazz + -Ar(t) dr

The constant ( Y ~ ~is' the polarisability element of the nonvibrating molecule and da,,/dr characterizes the manner in which the polarisability changes with r .

33

Substituting the expression for a,, into equation (7) the dependence of time fluctuations of both a and E becomes:

on the

I I

Using the identity cos 6 cos + = B[cos(O + +) + cos(6-@)] equation (10) becomes:

Equation (11) demonstrates that when a light wave interacts with a vibrating diatomic molecule the induced dipole moment, in this case exemplified by n;, has three components contributing to its time dependence. The first term on the right of equation (11) is a component vibrating with the frequency of the incident light and with a magnitude determined by azi’ and Ern,. According to classical electromagnetic theory an oscillating dipole radiates energy in the form of scattered light. Thus, as a result of the first term in equation (11)light of the incident frequency v,, will be emitted and will be observable in directions which differ from that of the incoming light. This is the phenomenon of Rayleigh scattering. The second term is a component vibrating at a frequency which is the sum of the frequencies of the light and the molecular vibration. The scattered light arising from this second term is known as anti-Stokes Raman scattering. The third term is a component vibrating at a frequency given by that of the light wave minus that of the molecule and the scattered light resulting from this term is known as Stokes Raman scattering. Both these components have magnitudes depending on the field strength of the light, the amplitude of vibration and the polarisability derivative da,,/dr. The appearance of scattered radiation, e.g. at vo + VGb, in units of Hertz arising from the second term in equation (ll),or vo-vvib from the third term in that equation, means that by analysing the scattered light we can monitor the vibrations within a molecule. It is this ability to measure molecular vibrations which gives the Raman effect its importance in the study of molecules. The information about molecular vibrational frequencies provided by infrared absorption spectroscopy is of the same kind as that provided by the VGb values of the Raman lines. However, Raman and infrared spectroscopies originate from two distinct physical processes. The Raman process is a scattering effect involving an induced dipole, a,which, in turn, depends on a change in molecular polarisability during a vibration. In contrast, infrared spectroscopy is an absorption process caused by a change in the permanent molecular dipole, p , with change in bond length during a vibration. Both infrared and Raman spectra are required to provide a complete picture of molecular vibrations. But because of the complementary nature of the effects only one technique may be applicable in a given instance. For

34

example Raman spectroscopy is often favored for biochemical studies because water has a relatively weak Raman spectrum (Fig. 4). In contrast the infrared absorption of water is very hgh in most of the region of interest and this often obscures the infrared absorption of the biochemical solute.

4. Raman and resonance Raman scattering; a quantum mechanical

interpretation The quantum mechanical approach to the scattering process is quite different to the classical model: the light beam is considered to be made up of packets or quanta of light particles known as photons, the quantisation of molecular energy levels is taken into account, and a means is provided for calculating the polarisability a,and thus Raman intensities, in terms of the electronic properties of a molecule. It is a reasonable approximation, for a gaseous diatomic molecule, to write the molecular energy E m ,as a sum of terms:

where the respective subscripts refer to electronic and vibrational components of the total energy. For present purposes the contributions due to molecular rotation and translation can be ignored. Electronic energy transitions involve much larger quantities of energy than vibrational transitions, with values of 10,000-50,000 cm-' for the former and 10-4000 cm-' for the latter. This situation is depicted in Fig. 5 with a large energy spacing between the ground and excited electronic states, and smaller spacings between the vibrational levels contained within each state. Moreover, for the vibrational energy, E,,, of a diatomic molecule it is a good approximation to write

where the vibrational quantum number u has only integral values so that the vibrational energy levels in the ground state in Fig. 5 are equally spaced by the amount vvib. The energy E,,, of course, takes the units of v,b, Hertz if the latter is expressed in Hertz and so on. In the quantum mechanical model light scattering is depicted as a two-photon process. The first step in t h s process is the combination of a photon and a molecule to raise the molecule to a higher energy state of extremely short lifetime. This state is reached by the upward arrows in Fig. 5 and as shown in the figure, the higher energy state may or may not correspond to a quantised energy state of the molecule. The second step, indicated by the downward arrows in Fig. 5, involves the release of a photon after a very short time interval (< lo-" sec). The energy of this second photon is given by the length of the downward arrows in Fig. 5. For Rayleigh scattering the upward and downward transitions have the same length and have

35

Upper (excited) electronic stote

3

Lower (ground) electronic state

2 I Infrared Rayleigh Normal Roman

Preresonance Roman

Resonance Roman

Fluorescence

n "

J

Fig. 5. Some of the possible consequences of a photon-molecule interaction. The lengths of the upward-pointingarrows are proportional to the frequencies of the incoming light while the lengths of the downward-pointing arrows are proportional to the frequency of the scattered (or in the case of fluorescence, emitted) light. The vibrational quantum numbers in the upper and lower electronic states are v' and v" respectively. The energy spacing v" between the lower state vibrational levels is equal to vmb. From [2].

therefore, apart from a change in sign, the same energies. Thus, in the Rayleigh process, no change in frequency of the photon occurs. The various kinds of Raman processes may now be outlined. If the downward arrow stops on a vibrational energy level that is higher than the starting level a Stokes process has occurred. In this, the second photon has a frequency vo-vvib corresponding to the third term in equation (11) of the discussion of the classical model for the Raman effect. Conversely, an anti-Stokes process results from the transition terminating at a lower vibrational energy level compared to the starting level. In the anti-Stokes process the second photon has an energy vo + v,+ giving the same result as the second term in equation (11). Of course, in both processes total energy is conserved so for Stokes scattering the molecule gains a quantum of energy vvib while for anti-Stokes scattering the reverse is true. For both Stokes and anti-Stokes processes a selection rule can be derived from equation (13) which says that v", in Fig. 5, can only change by k l . Thus equation (11) derived from the classical model agrees with the results obtained by considering quantised energy levels in that both models predict the difference in frequency between the incident and scattered light, vo-( vo-vvib), corresponds directly to the molecular vibrational frequency vvib. The quantum mechanical model also illustrates an important generalisation namely: that the position of Raman peaks is a property solely of the electronic ground state. This follows from the fact that vvib is a vibrational transition within the lower or ground electronic state in Fig. 5. In the classical model, equation (11) indicates no difference in the expected intensities of Stokes and anti-Stokes transitions, since the coefficients of the two

36

terms in the equation are the same. However, the model of quantised energy levels depicted in Fig. 5 shows that for anti-Stokes transitions to take place the molecule must be in a hgher (u” > 0) vibrational state within the electronic ground state. Since the population of these higher states is governed by a Boltzmann distribution only a small percentage of molecules are in higher vibrational states. The ratio of the number of molecules in the u” = 1 and u” = 0 vibrational states in the ground electronic state (Fig. 5) which we will denote Nl and No respectively is given by Nl = exp( - hv,,/kT) -

NO

where h is Planck’s constant, T is the absolute temperature and k is the Boltzmann constant. When T = 300 O K and the vibrational frequency is 480 cm-’, Nl is 0.1 No. As a result of the exponential nature of equation (14) an anti-Stokes line at 3 X 480 cm-’, or 1440 cm-I, would be 0.001 times as strong as the corresponding Stokes line. In practice this means that the feeble anti-Stokes scattering is usually ignored in conventional Raman spectroscopy and only the Stokes spectrum is recorded. Having outlined normal Raman scattering in which the energy of the incident light is considerably less than that needed to reach the higher energy electronic state in Fig. 5 the result of the light beam energy approaching that of the energy gap between the lower and higher electronic states can now be considered. In Fig. 5 the transition labelled ‘preresonance Raman’ is due to a light frequency that has almost enough energy to produce direct electronic absorption by the molecule. Under this condition the intensity of Raman scattering shows a marked increase. For normal or non-resonant conditions Raman intensities are proportional to the fourth power of the scattered light frequency, vs. However, as preresonance Raman conditions are approached the intensity of scattering goes up much more rapidly than u,”. A slight increase in the energy of the exciting radiation over that for the preresonance case will place the upward transition in Fig. 5 within the higher electronic state. Absorption of a photon can now occur and by the prompt re-emission of a second photon can give rise to the RR process. Band intensities in resonance Raman spectra can be orders of magnitude greater than those in normal Raman spectra. The reason for this can be seen by considering the quantum mechanical expression for Raman intensities. In the quantum mechanical treatment for randomly oriented molecules, the total intensity of the scattered light resulting from a molecular transition between states m and n is:

where I a,,, I m n is the transition polarisability tensor. This quantity can be derived from second-order perturbation theory to give

37

In these expressions the molecule is considered to be in the molecular state m. It is perturbed by an electromagnetic wave of frequency vo and intensity I , causing the transition to a state n and scattering light of frequency v, f vmn.The sum over index r covers all of the quantum mechanical eigenstates of the molecule, h is Planck’s constant, and r,. is a damping constant which takes into account the finite lifetime of each molecular state. The ( n I p,, I r ) , etc., are the amplitudes of the electric dipole transition moments where p,, is the electric dipole moment operator along direction p. Immediately, we see from equation (16) that as vo approaches the energy of an allowed molecular transition vrm, (vrm - vo ir,)becomes small and consequently one term in the sum becomes very large. This is the resonance condition. The intensities of various features in the RR spectrum are sometimes measured as a function of the excitation wavelength (usually in reference to an internal intensity standard). The intensity variation of a Raman mode with excitation wavelength is known as the excitation profile and can reveal a considerable amount of information regarding the electronic absorption transitions giving rise to RR intensity enhancement [5,6]. An important practical outcome of the resonance Raman effect is that the accompanying intensity enhancement allows one to obtain the Raman spectrum of molecules with suitable electronic absorption bands at low concentration, e.g. in the l op5 M range in solution. At the same time the resonance Raman effect enables the spectroscopist to selectively and specifically ‘pick out’ the Raman spectrum of an absorbing molecule in a complex environment which only contributes a weak normal Raman spectrum. This property is used to great effect in biologcal Raman studies since the chromophore is often found at the site of biological activity.

+

5. Polarisation properties of Raman scattering Most natural light is unpolarised, which in a simplified form means the electric ( E ) vector performs linear oscillations of constant amplitude in a plane perpendicular to the light path but that the orientation of the E vector within that plane is completely random. Light from lasers has the special property of being plane polarised; that is the terminus of the electric vector varies periodically within a single plane through the light path. Thus, for the plane polarised beam shown in Fig. 6 the E vector remains in the X Z plane but varies in magnitude along the light path according to the hatched lines. In Fig. 6 the laser beam is depicted as a vertical line starting at the bottom of the diagram. Information on the scattering process and on the assignments of Raman bands can be gained by analysing the scattered light parallel and perpendicular to the incoming E vector. The depolarisation ratio, p, of a feature in the Raman spectrum is defined as

where I, and Il arelthe intensities of Raman radiation of a given frequency that is polarised, respectively, perpendicular and parallel to the plane normal to the

38

Ill

Fig. 6 . The orientations of the E vectors of the incoming ( E ) and scattered light parallel (Ill) and perpendicular (IL) to the incident E vector. The depolarization ratio p = I , /Il,.From [2].

incident beam. These relationships are illustrated in Fig. 6. Changes in the polarisation of the incident light upon scattering result from the tensorial nature of the interaction denoted in equation (5). In fact for a single crystal the individual For fluids, however, elements of the scattering tensor a may be related to I , and I,,. the molecules are randomly oriented with respect to the laboratory-fixed coordinate system used to define a and when an average over molecular orientations is made, I , and Illare found to be related to certain combinations of the components of the tensor a. Detailed calculations show that for normal vibrations which do not preserve molecular symmetry during the motion of the nuclei (non-totally symmetric modes) p = 3/4. For modes which do preserve molecular symmetry p 5 3/4 and, in fact, p is often found to be substantially less than 3/4 for totally symmetric vibrations. Under resonance or near resonance Raman conditions in certain rare cases it is possible to observe ‘anomalously’ polarised bands with p > 3/4. T h s phenomenon is discussed in the literature [7].

6. Basic experimental aspects In a present-day Raman experiment intense monochromatic radiation provided by a laser is focussed onto or into the sample. In Fig. 7 the laser beam enters the sample in the vertical plane with the direction of its E vector shown by double-headed

39 x

MIRROR

ENTRANCE SLIT ~

SOLID ANGLE

Y

SAMPLE CELL

I

LENS

\

FOCUSING ~-

Fig. 7. The optics about the sample for a conventional Raman experiment. From [2].

arrows, Some of the resulting scattered light is gathered by collecting optics (seen as a single lens in Fig. 7) and directed to a dispersing system which is usually a double monochromator. The function of the spectrometer is to spatially separate the scattered light on the basis of frequency. At the exit port of the spectrometer the Raman spectrum forms an image in the form of a series of very faint lines. These are detected and recorded either sequentially by a single photomultiplier used with a scanning monochromator or simultaneously by a multi-channel detector which is the modern electronic equivalent of a photographic plate. The two options are shown schematically in Fig. 8. The basis of the dispersing process is depicted in Fig. 8 by a single monochromator although in most Raman experiments the dispersing process is repeated by linking two single monochromators to form a double monochromator. A double monochromator is often necessary to separate the Raman photons from the overwhelming number of Rayleigh photons. As shown in Fig. 8 there are two main ways in which the line spectrum across the exit port may be detected. The first and most commonly used method is to use a scanning spectrometer and to place a narrow exit slit over the exit port, followed by a photomultiplier tube. By slowly turning the grating, using the accurate drive of the spectrometer, the lines of the spectrum move in succession across the slit and are detected and recorded as outlined in Fig. 8. In the second method a multichannel detector is placed at the exit port. This detector is akin to having several hundred minute photomultiplier tubes across the port. All the Raman lines are then registered on different elements of the detector all the

40

Collection optics and sample

Slll

€7.11

SPECTROMETER

I

II

I

MEASUREMENT

1

Grating /

Image of spectrum1

\Photoactive surface

\

DETECTOR

Fig. 8. Schematic of a Raman spectrometer showing the options of single-channel (scanning) and multi-channel detection. From [2].

time. Thus, it is possible to observe the entire Raman spectrum on a TV screen or an oscilloscope in real time. When using multichannel detection the grating is turned only to change the spectral region across the detector.

7. Raman studies on biological materials Both the Raman and resonance Raman effects have been used extensively in biochemical studies [2-41 and it would be possible to divide the discussion under these two main headings. However, a more useful approach is to treat each class of biological material in turn and to show how Raman and resonance Raman experiments can provide different and often complementary information on its chemical properties. The three main classes of biological molecules to be considered are proteins, nucleic acids and lipids and membranes. 7.1. Proteins 7.1.1. Amide I and amide III features As can be seen in Fig. 9, the observed Raman spectrum of a protein recorded under non-resonance conditions consists of contributions from various amino acid side chain modes together with modes originating from the peptide backbone. Among the latter the amide I and amide I11 modes are widely used to characterise the secondary structure of the peptide backbone. The amide I modes have a high degree of C=O stretchmg character while the amide I11 modes have a large contribution from N-H in-plane bending. The use of the amide I and I11 regions in the Raman spectrum to characterise the secondary structure of a protein depends, in part, on determining characteristic frequencies for helical, P-sheet, p-turn and random protein conformations. Initially, the most widely used means of doing this was to use polypeptide models and proteins of known conformation [8]. The ranges within

41 T.0

Lysozyme Crystals

-

cm-' Fig. 9. A Raman spectrum of a protein, viz. the enzyme lysozyme in the crystalline phase. From [81].

which the amide I and amide I11 Raman bands occur for a-helical, P-sheet and unordered structures are given in Table 1. More recently the assessment of protein secondary structure from the amide I and I11 regions of the Raman spectrum has been made by a number of different approaches. In one of these, PCzolet and co-workers [9] have proposed a means of estimating the amount of P-sheet structure by using the relative intensity of the peaks at 1240 and 1450 cm-', due to the amide 111 and CH, bending modes (from the many CH, groups in the protein) respectively. The method is only applicable when there is a well-defined amide 111 band at 1240 3 cm-'. The 1450 cm-' feature is used, in Pkzolet's approach, as an internal intensity standard and this idea is common to the second method developed by Lippert et al. [lo]. In their method the relative intensities at 1240, at 1632 and at 1660 cm-' are taken to be a linear combination of contributions from a-helix, P-sheet and random coil conformations. The percentages of these conformations are derived from a set of four linear equations involving the intensity measurements as input data. The third method proposed by Williams [ l l ] for delineating the secondary structure of proteins analyzes the amide I band of a protein in terms of a linear TABLE 1 Approximate positions (cm-') of the most intense amide I and 111 bands in Raman spectra for various polypeptide conformations

a-Helix P-Sheet Unordered a

Amide I

Amide I11

1645-1 660 1665-1 680 1660-1 670

1265-1 300 1230-1 240 1240-1 260

Weak and may be confused with side-chain modes.

a

42

combination of amide I bands of proteins whose secondary structure is known. For 14 proteins analyzed by removing each one from the reference sets and analysing its structure in terms of the remaining proteins, the average correlation coefficients between the Raman and X-ray diffraction estimates of helix, P-strand, p-turn and undefined were 0.98, 0.98, 0.82 and 0.35, respectively. 7.1.2. Side chain contributions to the Raman spectrum 7.1.2.1. The disuljide group and -SH groups A relatively intense Raman line near 500-550 cm-’ is observed from the stretching mode, v ~ - of~ ,a disulfide linkage, CCS-SCC; and this feature can be seen in the spectrum of lysozyme shown in Fig. 9. The vs-s band can be used to follow changes in conformation about the SS linkage [2-41 (and see [12] for a recent discussion) and also, to follow the formation or breakdown of S-S bonds in proteins. Both cysteine (disulfide) and methionine groups in proteins give rise to C-S stretching vibrations in the 600-750 cm- regions. Hence, correlations proposed between vc-s and conformation within the -C-C-Smoiety in disulfide and methionine are easier to apply when only one group is present. The C-S stretching frequency has been suggested, on the basis of studies on dialkyldisulfides, to lie near 630-670 cm-’ when the site (X), trans to the sulfur atom, in

’

H

x-c- c -ss H

is occupied by a hydrogen, and 700-745 cm-’ when X is a carbon atom [13,14]. Contributions from C-S bonds are identified near 663, 696 and 721 cm-’ in the Raman spectrum of lysozyme (Fig. 9). The SH stretching band of cysteine residues occurs for proteins in the 2550-2585 cm-’ range. In one interesting application the intensity of the -SH feature has been used to follow the conversion of -SH to S-S linkages during the aging process of the lens from the eye of a rat [15]. 7.1.2.2. Tyrosine uibrations Tyrosine residues contribute peaks to the Raman spectra of proteins at 1617, 1210, 1180, 850 and 830 (the latter two form the so-called tyrosine doublet) and 645 cm-’; some of these features can be seen in Fig. 9. It was suggested by Yu et al. [16] that the ratio of the intensities of the tyrosine ring vibrations at 850 and 830 cm-’ (850/830 = R T y r )reflects ‘buried’ and ‘exposed’ tyrosines. Subsequently, it was shown that the doublet arises from Fermi resonance between a ring-breathing vibration and the overtone of an out-of-plane ring-bending vibration [17] and that the intensity ratio is sensitive to the nature of hydrogen bonding or state of ionization of the phenolic hydroxyl group. If the OH group is strongly bound to a negative acceptor RTyr is near 0.3. If the OH forms moderately strong hydrogen bonds to H,O, RTyr is approximately 1.25 and if the OH participates as a strong hydrogen bond acceptor RTy, is close to 2.5. For the -0- form of the phenol side chain RTyr is near 1.5. The doublet is seen in the spectrum of lysozyme at 836 and 856 cm-’ (Fig.9).

43

7.1.2.3. Ttyptophan modes Tryptophan’s 3-substituted indole ring can give rise to features near 1622, 1578, 1555, 1361, 1342, 1016, 880 and 762 cm-’ in the visible light excited Raman spectra of proteins and some of these features can be seen in Fig. 9. A sharp line at 1361 cm-’ has been suggested as an indicator of buried tryptophan residues [18]. Thus, the presence or absence of a line in this region in the spectrum of proteins containing tryptophan suggests buried or exposed tryptophans. In human carbonic anhydrase B whose four tryptophan residues are known to be buried, the Raman spectrum does indeed show a sharp line at 1363 cm-’ [19]. A line at 1386 cm-’ from deuterated tryptophan can be used to follow the kinetics of H/D exchange for tryptophan residues in proteins exposed to D,O. The rate of exposure of the tryptophan to the solvent due to the ‘opening and closing’ of the protein structure can thereby be calculated [20]. 7.1.2.4.Histidine vibrations The imidazole side chain of histidine often plays an important role in protein function. Unfortunately characteristic imidazole modes are rarely seen in protein Raman spectra. An extensive discussion of imidazole modes is given by Harada and Takeuch [12]. 7.1.2.5.Acid groups Although the -COOH moiety has a group frequency in the 1700-1750 cm-’ region, features in this part of the spectrum are rarely reported in the Raman spectra of proteins. However, a mode due to the ionised side chains, -COO-, is sometimes seen near 1417 cm-’ in the Raman spectra of proteins containing a hgh percentage of acidic amino acids. 7.1.3. Applications In recent years Raman spectroscopy has been used extensively to study the protein components found in the lens of an eye and the protein (and nucleic acid) components of virus particles. The reader is referred to the work of Yu et al. [15] and Ozaki et al. [21] concerning lens proteins and to section 7.5 for a discussion of the work of Thomas and associates [22] on viruses.

7.1.4. UV excited resonance Raman spectra of proteins After pioneering work using 250-350 nm excitation (see [2], pp. 96-98, for a summary), the mid 1980’s has seen a surge of interest in the 200-230 nm UV range excited RR spectra of proteins. Pulsed laser light in this regon is usually generated by nonlinear frequency doubling and mixing of a dye laser output or doubled output with the 1.06-pm YAG fundamental; with a H, or D, Raman shifter being used to reach the lower wavelengths. The present high activity in the 200-230 nm UV excited RR spectra of protein presages many new findings. At the present time the following generalisations are emerging: 1. The excitation range below 230 nm is better than the 230-300 nm region from the point of view of having minimal interference from fluorescence. 2. Tryptophan and tyrosine chromophores can be selectively excited by 218 or 200 nm irradiation, respectively. 3. Amide I, 11, and I11 features are seen in the UV excited RR spectra, unlike the normal Raman case where amide I1 bands are usually too weak to be observed.

44

4. Care has to be taken to control unwanted photochemistry caused by the short-lived, intense UV excitation pulses [23]. Up to mid-1985, the UV-laser excited Raman spectra have been reported for peptide backbone model compounds acetamide and N-methylacetamide [24], insulin and a-lactalbumin (218 and 200 nm; [25]), myoglobin (230 nm; [26]), hemoglobin (218 and 200 nm; [27]), and cytochrome c (218 and 200 nm; [28]). 7.2. Proteins containing a natural, visible chromophore

Most protein-bound chromophores absorbing light in the 350-700 nm region have been the subject of RR study. There is extensive literature concerning RR investigation of proteins containing hemes, visual pigments and their bacterial analog bacteriorhodopsin, metal ions, flavins, chlorophylls, and carotenoids. Table 2 summarises the kind of information obtainable for each class of chromophore. In every case the RR spectrum contains detailed chemical information on the chromophore and usually the RR spectrum is uncluttered by contributions from the protein matrix or other species present. In a sense the RR spectrum can be regarded as a vibrational (and highly informational) counterpart of an electronic absorption spectrum and the concentrations used to obtain RR and absorption spectra are normally in the same range as those used to obtain routine absorption spectra, typically 10-4-10-6 M in chromophore. The discussion in the rest of this section will focus on some aspects of heme protein-RR spectroscopy. Hemes are by far the most widely studied chromophore and can be used to illustrate the degree of detail which may be elicited from RR spectra. A typical heme absorption spectrum is shown in Fig. 10. RR spectra can be generated by exciting into the Soret region near 400 nm or into the a-p bands in the 500-570 nm wavelength range. The structure of RR spectrum depends markedly on the excitation region employed. Excitation into the a-/3 region produces intense RR bands which are either depolarised ( p = 0.75) or anomalously polarised ( p > 0.75). Some early high quality RR spectra, excited in or near the /3 electronic transition, of a cytochrome and a hemoglobin are shown in Fig. 11. The spectra are dominated by peaks in the 1100-1650 cm-' region, because these peaks are due to the in-plane stretching of C-C and C-N bonds and the bending of C-H bonds which are effective in vibronically mixing the in-plane a and Soret electronic transitions to create the j3 band. Several peaks in Fig. 11have high utility as marker bands. For example the so-called band I, which occurs between 1358 and 1377 cm-' can be used as an oxidation state marker for the Fe atom. Band IV, which occurs between 1552 and 1590 cm-' is easily recognised by its high intensity and anomalous polarisation (Fig. 11). Band IV has great value in that its position correlates with the Fe-porphyrin core size as defined by the Fe-N (porphyrin ligand) distance [29]. These and other marker bands have been used to follow the details of chemical changes in a wide variety of heme proteins under a wide variety of conditions [30]. Excitation into the Soret band often enables one to detect RR bands in the lower frequency range, 100-800 cm- which are associated with Fe-axial ligand motions.

',

45

In one study Kitagawa and colleagues [31] identified the Fe-histidine stretching peak in the 214-225 cm-' region for various mutant deoxyhemoglobins. Separate oxygen binding experiments enabled them to obtain K,, the 0, equilibrium binding TABLE 2 A summary of resonance Raman studies on natural chromophores in the visible spectral region Biochemical class

Examples

Chromophore

Typical information

Hemes

Hemoglobin a Myoglobin Cytochrome c a,c Cytochrome P-450 Horseradish peroxidase Cytochrome oxidase

Usually porphyrin moiety, occasionally charge transfer transition involving porphyrinbound metal may contribute

Fe spin and oxidation state 8 Fe-N (from tetrapyrrole) core size g Fe-axial ligand chemistry 8 Protein and poryphyrin relaxation following photolysis of Fe-CO Quaternary structure transitions '

Visual pigments and bacteriorhodopsin

Rhodopsin Bacteriorhodopsin Halorhodopsin

Retinal, covalently linked to protein as Schiffs base

For each intermediate in photocycle: conformation of polyene and state of protonation of Schiffs base

Metalloproteins

Hemerythrin m.n Hemocyanin Tyrosinase Ribonucleotide reductase O Ferridoxin Andrenodoxin Rubredoxin 'Blue' copper Transferrins and other Fe(II1)-tyrosinate proteins "

Metal ligand(s) chargetransfer transition

Identification and coordination geometry of metal ligands

Flavoproteins

Yeast fatty acyl-CoA oxidase ' Porcine liver fatty acylCoA dehydrogenase Yeast glutathione reductase ' Egg-white flavoprotein " Old yellow enzyme " D-aminO acid oxidase NADPH-cytochrome P450 reductase '

Flavin

Type of bonding between flavin and protein. Chemistry of charge-transfer complexes involving flavin and second ligand (e.g. phenol " or amino-acid derivative ")

J

'

Table 2 continued on next page.

Ir

46

TABLE 2 (continued) Biochemical class

Examples

Chromophore

Typical information

Chlorophylls

Chlorophylls Chloroplasts Algae Reaction centers

Tetrapyrrole

Selectively obtain RR spectra of e.g. chlorophyll a and b in situ. Nature of binding site in protein. Mg coordination number

Carotenoids

Many in vivo situations bb e.g. photosynthetic membranes '' lobster shells

Polyene

Polyene conformation; polyene-polyene exciton interactions; membrane potential; triplet state properties ee

Phytochrome

Isolated bile pigments

Biliverdin dimethyl ester

Conformation

f f

For references see pp. 63-64.

constant for each mutant hemoglobin. Kitagawa et al. were then able to show that v ~ correlates ~ remarkably ~ ~well with ~ K, (Fig. 12). The variation in v ~ was ~ attributed to strain imposed on the Fe-histidine bond by the globin. Measurements such as these provide key evidence on the mechanics of hemoglobin function. In another study involving excitation into the Soret band Yu and his co-workers [32] have challenged the detailed X-ray crystallographic analysis of a heme protein. A fragment of the 406.7 nm excited RR spectrum of CO bound to the monomeric

Y

A (nm)

Fig. 10. Absorption spectrum of cytochrome c in the reduced form.

-

-

0-

h

1.

Y

h

INTENSITY

0 v

41

B 6'

5a

E. *

Fig. 11. Resonance Raman spectra of (a) ferrocytochrome c , 0.5 mM obtained with 514.5 nm excitation and (b) oxyhemoglobin, 0.5 mM, obtained with 568.2 nm excitation. From [7b].

hemoglobin I11 from Chironomzrs thummi thummi is shown in Fig. 13. The isotopic substitutions identify the Fe(I1)-CO stretching mode at 500 cm-' and the Fe(I1)-C-0 bending mode at 574 cm-'. Similarly in the complex involving CN-, Fe(II1)-C-N- stretch and Fe(JI1)-C-N- bend were assigned at 453 cm-' and 412 cm-', respectively. The RR data, in conjunction with those obtained from heme model complexes with known Fe-C bond distances, suggested strongly that the

48

K,/(mmHg)

Fig. 12. Correlation between the Fe-His stretching frequency, mutant deoxyhemoglobins. From [31].

Y,

and oxygen affinity K , for various

A)

Fe(II1)-CN- bond ( - 1.91 is longer (hence weaker) than the Fe(I1)-CO bond This result is at variance with the X-ray crystallographic findings of 2.2 and 2.4 A for the Fe-CN and Fe-CO bonds, respectively; leading Yu to suggest that there may have been errors in the X-ray crystallographic refinement. ( - 1.80

A).

7.3. Resonance Raman labels The advantages of the RR effect are that it provides specificity and selectivity in very complex biological systems at chromophore concentrations in the 10-3-10-6

*

Hb CTT 111. CO

407

489

I

I

300

400

cm-'

I

I

500

600

Fig. 13. CO isotope effects on the resonance Raman spectrum of a heme protein with a CO molecule bound to the porphyrin Fe atom. From [32].

49

M range. However, many sites of high biological interest do not have suitable chromophores to act as RR probes. For these, the RR labelling technique was developed [33]. A RR label, usually mimicking a natural component, is introduced into the system as a reporter group and there has been success in using chromophoric ligands to study antibody-hapten, enzyme-inhibitor (and drug), DNA-drug and cell-dye interactions [34]. The great majority of studies have involved protein-chromophoric ligand interactions. Recently, the labelling technique has been used extensively to monitor the chemical details of enzyme-substrate complexes. One approach is to use substrates which are themselves chromophoric [33,35], in another approach the chromophore is formed at the point of the transient covalent linkage between the substrate and the enzyme. The latter method relies on a reaction involving the hydrolysis of thionoesters (which may be based on a single amino acid or a multipeptide complex) by cysteine proteases such as papain. The hydrolysis of the thionoester substrate

N

U

-

O N

cch.

0

II

Ph - C - N H

S -CH2-

II

C -S-C-PAP

Fig. 14. Monitoring the group (and its neighbors) undergoing transformation in an enzyme’s active site. The resonance Raman spectrum shown is of the enzyme substrate transient PhC( = O)NHCH,C( = S)SPapain, 324 nm excitation; data acquisition time is 10 sec. From [82].

50 TABLE 3 Information

Method

Number and types of substrate conformers in active site

Identified using a library of structure-Raman spectra correlations

Search for geometric strain in bound substrate

By comparing RR spectra of enzyme-substrate intermediate with those for model compounds in standard state

Molecular information on individual kinetic rate constants

By combining RR and kinetic data

Conservation of catalytic mechanism during evolution

By comparing RR data for plant and mammalian cysteine proteases

Effects of enzyme-contacts far from points of catalyses

By investigating the effects of substrates of increasing sue on the RR spectrum of the enzyme-substrate linkage

Different species on the reaction pathway

Rapid mixing-rapid flow system using RR detection

Enzyme-substrate dynamics

Study intermediates under cryoenzymological conditions

RC(=O)NHCHR’C(=S)OCH, occurs via the formation of a transient dithioester RC(=O)NHCHR’C(=S)-S-papain, where the thiol sulfur is the S of cysteine 25 in papain’s active site. The dithioester is chromophoric absorbing near 315 nm and gives rise to a label just at the time and place of catalytic transformation. A natural intermediate in the hydrolysis of an ester or amide linkage is a thiol ester -C(=O)S, so the RR label involves substituting a C=S for a C=O group. The 324 nm excited RR spectrum in Fig. 14 shows how different spectral features monitor conformation in different parts of the enzyme-substrate complex near the scissile bond. The type of information gained by studying such complexes is summarised in Table 3 [ 36- 381. 7.4. Nucleic acids 7.4.1. The purine and pyrimidine bases The normal Raman spectrum of a polynucleotide contains approximately 30 detectable bands. Nearly all of these are due to purine or pyrimidine ring modes and the prominence of the base ring modes has led to detailed analysis of their vibrational spectra. The ring modes can be used to gain a semi-quantitative estimate of base content in a heteropolynucleotide, to monitor C-H C-D exchange on the rings [39] and to follow protonation of the bases. Protonation can even be detected for a small percentage of the total bases in RNA encapsulated in a virus [40]. In addition to the base modes, two important features originating from the phosphate group have been identified near 800 and 1100 cm-’ and are dealt with in the following section. The ribose or deoxyribose groups are poor Raman scatters and do not contribute any

51

cm"

Fig. 15. Raman spectra of H,O and D,O solutions of poly(rA). poly(rU) at 32 and 85°C. From [43].

intense or moderately intense features to the spectrum. However, in the case of guanosine it has been demonstrated recently that the guanine ring-breathing frequency near 650 cm-' is sensitive to conformational events in the sugar and the glycosidic linkage [41]. In both DNA and RNA certain purine and pyrimidine ring modes are sensitive to base-pairing and base-stachng interactions. Some of these features, and the general appearance of polynucleotide spectra, are illustrated by the spectrum shown in Fig. 15 of poly(rA)poly(rU), a double helix in which the adenine residues of poly(rA) hydrogen bond to the uracil residues of poly(rU). The system was initially investigated by Small and Peticolas [42] and independently by Lafleur et al. [43]. As Fig. 15 shows, marked spectral changes occur upon raising the temperature from 32 to 85 " C. The spectral changes result from the thermal disruption of the helix with, at high temperature, the almost total loss of the base-pairing and base-stacking interactions. Key spectral changes in Fig. 15 are intensity variations of certain ring modes and the radical changes in the carbonyl profiles between 1650 and 1700 cm-'. In the latter region in D,O at 85 C the carbonyl groups of U give strong lines at 1661 and 1696 cm-' while at 32°C a single line occurs at 1688 cm-'. Several lines, assigned to A and U ring vibrations, show appreciable intensity loss upon helix formation at32°C. This is called Raman hypochromism [44,45]. The phenomenon has a direct correspondence with the hypochromism observed in the UV adsorption spectrum and is believed to arise from the electronic interactions between vertically stacked bases. A few lines, however, show modest intensity gain in the 32" C spectrum (e.g. the mode near 1570 cm-' increases in intensity with increasing structural order) and this effect is termed Raman hyperchromism. O

52

Similar effects are seen in the spectrum of the poly(rC)poly(rG) complex. Again there are several hypochromicities and a notable hyperchromic band at 670 cm-' due to a G ring mode.In poly(rC)poly(rG), however, the intensities of lines in the carbonyl region are weaker, by a factor of 6-8, compared to the carbonyl modes in the A.U. helix. It is tempting to make the assumption that in a RNA containing a heterogeneous sequence of bases the carbonyl region may be used to quantitate-base pairing and the purine and pyrimidine ring modes may be used to form a semi-quantitative picture of base stacking. However, difficulties arise from the fact that the profile in the carbonyl region and the degree of hypochromism are both independent upon base sequence. Moreover, some hyperchromic or hypochromic lines may reflect base pairing as well as stacking interactions [46]. 7.4.2. Conformation of the (deoxy)ribose-phosphate backbone The phosphate groups:

in the (deoxy)ribose-phosphate backbone of RNA (and DNA) give rise to two characteristic Raman bands near 800 and 1100 cm-' whch are very useful probes of backbone conformation. The 800 cm-' feature is assigned to the -0-P-Osymmetrical stretching vibration [47] while the 1100 cm-' band originates from the PO; symmetric stretch motion. Conformational utility stems from the fact that the frequency and intensity of the PO, feature is insensitive to backbone geometry, and thus provides an internal standard, while the 800 cm-' is highly sensitive to conformation of the -C-0-P-0-Cgroup and possibly the ribose ring [48,49]. The Raman spectrum of an ordered, single-stranded or double-helical RNA shows an intense sharp band at 810-815 cm-' which shifts to near 795 cm-' upon disordering. This transition is clearly seen in the spectrum of poly(rA)poly(rU) in Fig. 15 while the same spectrum demonstrates the insensitivity of the 1100 cm-' feature to disruption of secondary structure. The intensity of the PO; Raman mode remains constant at constant ionic strength. For RNA, at low ionic strength, the ratios of intensities of the bands at 851 and 1100 cm-' can be used to monitor the amount of secondary structure. Z(815)/( I(1100) = 1.66 in completely ordered ribopolymers (double-helical or single-stranded) and 0.0 in completely disordered ribopolymers [50]. The phosphate modes for DNA resemble those for RNA; the DNA 1100 cm-' band is insensitive to changes in secondary structure and, as in the case of RNA, the features near 800 cm-' in the Raman spectra of DNA are sensitive to conformation. For DNA in solution or cast as a fiber the 800 cm-' band can be used to characterise the A, B [51] and Z [52]forms of DNA and to follow fluctuations in the sugar conformations [53].

53

7.4.3. Resonance Raman studies of nucleic acids The nucleic acid bases have a rich assortment of electronic transitions in the 200-300 nm range. These absorption transitions are being increasingly exploited to provide RR spectra. In turn the RR spectra, via their excitation profiles, can help identify some of the often controversial features in the electronic absorption spectra [54,55]. The most detailed analysis of the RR spectra of nucleic acids appears in the review by Nishimura et al. [56], where these authors discuss a normal coordinate treatment of nucleic acids together with RR theory and experimental results. Several approaches have been used to generate UV laser light. Early studies used 257.3 nm obtained by frequency doubling the 514.5 nm cw argon laser line [56], sources in the 267-305 nm were then accessed using a frequency doubled pulsed dye laser [54,55]. More recently harmonics of the YAG laser output and their H, or D, Raman shifted frequencies have been used in the 200-266 nm range [57,58].

N

dAMP

W

0

2Wnm x 0.33

200nm

1

600

1

1

800

1

1

1

1

1000 1200

1

1

1400

1

1

1600

1

1

I800

A cm-' Fig. 16. Resonance Raman spectra of aqueous, 5 mM, deoxyadenine 5'-monophosphate. The different excitation wavelengths used for each spectrum are indicated. From [SS].

54

The excitation wavelength dependence of the RR spectrum of deoxyadenine 5’-monophosphate is illustrated in Fig. 16. Quite pronounced changes in the appearance of the RR spectrum occur and these can be understood on the basis of the five calculated T-T * electronic transitions of adenine in the 200-266 nm region [58]. The strong wavelength dependence seen for adenine is also found for the other bases and this behavior holds promise for selectively exciting the RR spectrum of a given class of base in a complex polynucleotide structure. The enhancement variations also assist the spectroscopist in resolving overlapping components and in making vibrational assignments. The substitution of a bromine atom on a nucleic acid base (e.g. 8Br-adenosine) provides the base with significant absorption in the 300 nm region. The RR spectrum of the brominated species can then be specifically excited by 300 nm irradiation [59]. The brominated bases are in effect RR labels but there are rare naturally occurring bases with significant absorption in the near UV, these are sulfur substituted analogs absorbing from 300-360 nm. For example Nishimura, Tsuboi and coworkers [60] obtained RR spectra of the single 4-thiouridine which occurs in a number of tRNAs. 7.5 Viruses

Raman spectroscopy has yielded detailed molecular information on several viruses and other DNA and RNA complexes (see [2] pp. 198-201). Here, one recent example, the RNA-based cowpea chlorotic mottle virus [61], will be discussed since it illustrates the wealth of detail which may be gained from the Raman spectrum. At the same time the study provides examples of the conformationally sensitive RNA and protein features mentioned in the foregoing sections. Cowpea chlorotic mottle virus is an icosahedral RNA virus made up of three nonidentical ribonucleoprotein particles. The Raman spectra of the intact virus and its individual component protein shell (capsid) and RNA parts are shown in Fig. 17. The base and backbone contributions are identified in the spectrum of the RNA while the amide, CH, and CH, contributions are indicated in the spectrum of the protein. Most of the other features in the capsid spectrum can be assigned to aromatic side chain modes. By analysing the small spectral differences observed as a function of pH and by comparing the spectrum of the intact virus by difference spectroscopy with spectra of capsids, subunit dimers and protein-free RNA, Thomas and his coworkers [61] have demonstrated that a good deal of detailed information may be obtained: a. For the RNA in the virus, the carbonyl stretching region and the purine and pyrimidine ring modes indicate that the bases are paired and stacked. The relative intensity of the -0-P-0- and PO; modes shows that the backbone of encapsulated RNA is in the conventional C3’-endo geometry. b. The proteins’ amide I and 111 profiles show that the predominant secondary structure in the virion is /3-sheet. c. Two features are seen at 2551 and 2571 cm-’ in the -SH stretching region, with the former band being broad and assigned to -SH groups in a H-bonding

55

Virus

Capsid

I

C

"I

R NA

Fig. 17. Comparison of the Raman spectrum of an intact virus (top) and its protein (capsid) and RNA components. From [61].

d.

e.

f.

g. h.

environment. The 2571 cm-' band is ascribed to the remaining cysteine chains in a hydrophobic environment. The tyrosine doublet indicates that the tryosine side chains exist on average with the p-hydroxy groups in contact with hydrogen-bonding donor and acceptor groups. Differential tryptophan and phenylalanine ring intensities suggest that these residues are in different environments in the virion and capsid states and, thus, that these aromatics are involved in interactions with the RNA. Changes in bands from C-C, -CH,- and -CH, groups in the 1130 and 1340 cm-' regions show that configurations in the aliphatic side chains are altered upon release of the RNA from the virion. There are changes in both protein and RNA backbone conformations upon dissociating the RNA from the capsid. Swelling of the virion by increasing the pH from 5.0 to 7.5 has no effect on aspartate and glutamate -COOH features and thus does not titrate these groups. However, small numbers of Ade+ and Cyt residues become deprotonated. The protonation of bases in the virion at pH 5.0 is limited to adenines and cytosines. +

i.

56

7.6. Lipids and membranes

Both Raman and infrared spectroscopy provide a wealth of molecular detail on the conformational and dynamical properties of model and real biological membranes. The infrared and Raman methods are complementary and often mutually supportive, but in keeping with the theme of this chapter just the Raman technique will be discussed here. Raman spectroscopy has the capability of monitoring both inter- and intramolecular interactions in membrane assemblies and for identifying the part of the lipid molecule undergoing a particular perturbation. Fig. 18 shows many of the conformationally sensitive features. The headgroup region can be probed via the symmetric C-N and PO, modes near 717 and 1243 cm-', respectively, and the carbonyl environments by their modes near 1720 and 1740 cm-'. The Raman skeletal C-C stretching vibration region between 1050 and 1150 cm-' enables one to monitor the truns/guuche conformational ratio, within the acyl chains, while intermolecular chain packing properties can be followed by intensity changes in the C-H stretching region from 2800-3100 cm- The methylene deformation region near 1450 cm-' can also be used to follow changes in intermolecular order. The C-C and C-H stretching regions are the most often used as probes of membrane structure and they will be discussed in more detail.

'.

Liquid crystalline;

1

I

1

520

1

1

840

h

40°C

1

1

1160

cm-'

1

1

I480

I

I

1800

Fig. 18. Raman spectra of dimyristoyl phosphatidylcholine in the gel and liquid crystalline states. From ~31.

7.6.1. The C-C stretching region between 1050 and 1150 cm-' This region contains vibrations in which alternate carbon atoms move in opposite directions along the chain length. There are at least three bands which exhibit marked changes upon disordering of the hydrocarbon chain. These can be seen in Fig. 18 for dimyristoyl phosphatidylcholine going through the gel-to-liquid crystalline transition. The intensities of the two strong lines near 1128 and 1064 cm-', assigned to skeletal optical modes of all trans conformers, decrease abruptly as the melting temperature ( T m )is approached. Plots of intensity of the 1128 cm-' feature (normalised with respect to a temperature invariant band) vs. temperature for many systems reveal that the type of transition seen in Fig. 18 is highly cooperative. The temperature dependence of the spectra, in the 1000-1200 cm-' region, of a variety of phospholipids have been studied by a number of groups and there have been attempts to extract quantitative information on lipid behaviour using the feature near 1130 cm-' [62]. However, as Levin has pointed out [63] the difficulties in extracting quantitative information are formidable due to such factors as coupling of the 1130 cm-' mode to the terminal methyl rocking mode at 892 cm-', underlying features in the 1100 cm-' region and problems in normalising the various parameters involved. Even with these difficulties temperature profiles constructed from the intensity ratios of the 1085-1090 and 1130 cm-' features, provide a convenient method for following gel-to-liquid crystalline phase transitions. An increase in the 1090,4130 cm-' ratio denotes an increase in chain disorder through the introduction of gauche bonds. 7.6.2. The C-H stretching region between 2800 and 3000 cm-' This spectral range contains C-H stretching modes from the phospholipids' methylene and methyl groups. The relative abundance of the methylene group results in -CH,- modes dominating the C-H stretching region. This is evidenced by the Raman spectrum, between 2800 and 300 cm- ',of diarachidoyl phosphatidylcholine shown in Fig. 19, where the intense peaks near 2847 and 2883 cm-' are assigned to the methylene symmetric and asymmetric stretching modes, respectively. The weaker band near 2936 cm-' is assigned, in part, to the chain terminal CH, symmetric stretch. Although these assignments establish the origin of the 'sharp' features seen in the C-H stretching region there has been considerable effort recently to elucidate the origins of the broad band or bands underlying the resolved peaks. An understanding of these broad bands is essential to the correlation of spectral with conformational and environmental change 1631. The sensitivity of the C-H region to conformational change is demonstrated in Fig. 19 which compares the Raman spectra of dispersions in the gel and liquid crystal states. As the temperature is raised and the gel state bilayer disorders and reaches the liquid crystalline state there is a marked change in the feature near 2880 cm-I. It decreases in intensity, broadens and shfts by + 10 to 12 cm-I. Although a number of spectral changes may be used, many authors have used the peak height to follow gel-to-liquid crystalline phase intensity ratio Z2ss5/I,,5, (or 12885/12935) transitions. In general, increases in peak intensity of the 2935 (or 2850) and 2880 cm- bands reflect intermolecular chain disorder and order, respectively.

58

;

Liquid crystalline

1

I

I

I

I

I

I

I

2800 2842 2885 2928 2971 3014 3057 3100 cm-’

Fig. 19. Comparison of the Raman spectra, in the C-H stretching region, of diarachidoyl phosphatidylcholine in the gel and liquid crystalline states. From [63].

7.6.3. Deuterated lipids as selective probes In multicomponent systems difficulties arise from the overlapping of C-H features due to chemically different lipids, or in lipid-protein arrays, from protein C-H stretching bands. In these systems it becomes impossible to monitor a single lipid component. Mendelsohn et al. [64] showed how this problem can be overcome by the use of deuterated components. They inserted a completely deuterated fatty acid into a model membrane system and followed the C-D stretching vibrations in the spectral window 2000-2220 cm-’ which is uncluttered by modes from other Components. As the membrane passed through a gel-liquid crystal transition the line-width of the C-D stretching vibrations of the bound fatty acid was found to be a sensitive probe of membrane polymethylene chain order. Selective deuteration provides information on band assignment [65,66] and a probe of conformation within a single phospholipid. B a n d et al. [67] studied the temperature dependence of the Raman spectra of 1,2-dimyristoyl-sn-glycero-3-phosphocholines specifically deuterated in the 2 chain at positions 3, 4, 6, 10, 12 and 14. These authors showed that the frequencies of the CD, stretching modes depend on the position of the CD, label, being maximum at position 3 and decreasing until they become constant beyond position 6. The degree of the observed increase in the width of the C-D bands at T, is also position dependent. An interesting example of selective deuteration is the work of Gaber et al. [68] which involves deuterating the 1 chain or the 2 chain of dipalmitoyl phosphatidylcholine. Differences in the spectral characteristic of the compounds containing the perdeuterated 1 chain or the

59

perdeuterated 2 chain at a certain temperature were noted. These differences were attributed to nonequivalent conformations of the fatty acid chains at positions 1 and 2; below the pretransition chain 2 appears to depart slightly more from the all-trans structure than chain 1. 7.6.4. Lipid protein interactions and natural membranes The interaction of lipids with small entities such as cholesterol [69] and metal ions I701 has been studied extensively by Raman spectroscopy. The effect of the perturbants has been followed via the lipids' C-C and C-H stretching regions. Recently, more attention has been focussed on lipid protein interaction, again the C-C and C-H regions are crucial to following changes in lipid properties, but now protein features, such as the amide I and I11 modes, may be recognized in the Raman spectrum [71] and analysed according to the precepts set out in the discussion of protein spectra above. In one study Taraschi and Mendelsohn [72] formed lipid-protein complexes from dipalmitoyl phosphatidylcholine (and its perdeuterated analog) and glycophorin, a protein isolated from erythrocyte membranes. The temperature dependence of the C-D stretching region of the protein-lipid complex showed that at a lipid protein mole ratio of 125 : 1, a broad melting event occurs whose midpoint is about 15°C lower than that for the pure lipid. Using their earlier postulates concerning C-D linewidth and gauche population [73] the authors concluded that the same number of gauche isomers form in the phospholipid hydrobcarbon chains during the melting process as in the phase transition of the pure lipid. There is special interest in the nature of interactions at the lipid-protein interface and Taraschi and Mendelsohn point out that the conformation of the lipid at the interface is markedly changed by the interaction. Moreover, the Raman results enable them to infer for the 125: 1 sample that the perturbation extends well beyond one shell of lipid molecules and must be at least four to five layers deep. Lavialle et al. 1741 have also obtained information on the lipid-protein boundary. These authors studied the interaction of melittin, a polypeptide consisting of 26 amino acid residues, with dimyristoyl phosphatidylcholine. The results illustrated in Fig. 20 show that for a lipid-melittin molar ratio of 14: 1 two order-disorder transitions are observed, one above (at 29°C) an$ one below (at 17°C) the transition for the pure lipid (at 22.5 " C). The low temperature transition is associated with a depression of the main lipid phase transition while the 29 " C transition is associated with the melting behavior of approximately seven immobilized boundary lipids which surround the hydrophobic portion of the melittin. The application of Raman spectroscopy to naturally occurring membranes is hindered by problems such as background luminescence, or the sheer complexity of the system. However, several groups have been able to obtain Raman spectra from natural membranes. The most extensively studied system is the membrane from human erythrocytes, commonly known as red blood cells [75-771. Lippert et al. [75] examined the membranes from human red blood cells, which had been repeatedly washed to remove traces of fluorescent material. The Raman signatures of both protein and lipid components were observed and from the amide I' (in D,O) and

60


1.4

I

0.6 0

4

8

12

16

18

24

28

32

36

40

T (OC) Fig. 20. Temperature profiles for dimyristoyl phosphatidylcholine-melittin liposomes using the I,,,o /I113o ( I g I I U e h e / I , l a npeak S ) height intensity ratio as a marker. (-A-) 14.1 lipid-melittin ratio: (- - -) pure lipid bilayers. From [74].

amide I11 regions of the protein spectrum the protein fraction was estimated to be 40-55% a-helical. From an analysis of the 1100 to 1150 cm-' region the authors showed that about 60% of the lipid hydrocarbon chains were in the all-trans form. Verma and Wallach have published several contributions on the erythrocyte system. By monitoring the C-H stretching region they observed the main gel to liquid-crystal transition of the lipids near - 8" C [76] and they also reported evidence for a pH-sensitive transition in the physiological temperature range [77]. A further approach to studying the properties and function of natural membranes is the use of RR probes, either intrinsic or extrinsic. Carotenoids are known to be an important natural constituent in the membranes of photosynthetic bacteria. Koyama et al. [78] have shown that the RR spectra of carotenoids in these membranes can be used as sensitive probes of membrane potential. Changes in electrical potential cause small shifts in carotenoid absorption maxima but with judicious choice of RR excitation wavelength, small changes in X max can give rise to large changes in the intensity ratio of the carotenoids' vl and v2 modes (near 1526 and 1157 cm-', respectively). Thus, the intensity ratio of v 1 and v2 becomes a sensitive measure of trans-qembrane potential and Koyama et al. were able to observe oscillation in the potential across the membranes of photosynthetic cells under growing conditions. Another interesting example of the use of a polyene RR spectrum involves the extrinsic probe amphotericin B. The latter molecule is a polyene antibiotic containing seven conjugated double bonds. It was possible to follow changes in both the RR spectrum of the antibiotic and the normal Raman spectrum of lipid as a function of temperature in various lipid and lipid-cholesterol systems [79]. Amphotericin B could be regarded as a RR label and there is another example of where a RR label has been used to follow membrane properties. The second example involves the dye quinaldine red and the intact cells of the bacterium S. faecalis [SO]. The RR spectrum of the free dye changes upon binding to the membranes of the resting (non-metabolising) cells and changes again when the cells

61

are provided with glucose as an energy source and the membranes become energised. In the first instance, RR band frequency and intensity changes occur and these effects are ascribed to ionic interactions between dye and components of the resting membrane. Only the intensities of the RR bands change upon energisation and these changes are ascribed to dye aggregation.

References 1 Raman C.V. and Krishnan, K.S. (1928) Nature (London) 121, 501. 2 Carey, P.R. (1982) Biochemical Applications of Raman and Resonance Raman Spectroscopics. Academic Press, New York. 3 Tu, A.T. (1982) Raman Spectroscopy in Biology: Principles and Applications. John Wiley, New York. 4 Parker, F.S. (1983) Applications of Infrared, Raman and Resonance Raman Spectroscopy in Biochemistry, Plenum Press, New York. 5 Siebrand, W. and Zgierski, M.Z. (1979) In: Excited States (E.C. Lin, ed.), Vol. 4, Ch. 1, Academic Press, New York. 6 Clark, R.J.H. and Stewart B. (1979) Structure Bonding (Berlin) 36, 1-80, 7 (a) Placzek, G. (1934) In: Rayleigh and Raman Scattering, UCRL Transl. No. 526L; from: Handbuch der Radiologie (E. Marx, ed.), Vol. VI, Part 2, pp. 209-374, Akademische Verlagsgesellschaft, Leipzig. (b) Spiro, T.G. and Strekas, T.C. (1972) Proc. Natl. Acad. Sci. USA 69, 2622-2626. 8 Frushour, B.G. and Koenig, J.L. (1975) Raman spectroscopy of proteins. Adv. Infrared Raman Spectrosc. 1, 35-47. 9 PCzolet, M., Pigeon-Gosselin, M. and Coulombe, L. (1976) Biochim. Biophys. Acta 453, 502-512. 10 Lippert, J.L., Tyminski, D. and Desmeules, P.J. (1976) J. Am. Chem. SOC.98, 7075-7080. 11 Williams, R.W. (1983) J. Mol. Biol. 166, 581-603. 12 Harada, I. and Takeuchi, H. (1986) Advances of Spectroscopy of Biological Systems (R.J.H. Clark and R.E. Hester, eds.) 13, 113-175. 13 Sugeta, H., Go, A. and Miyazawa, T. (1972) Chem. Lett. p. 83. 14 Bastian, E.J. and Martin, R.B. (1973) J. Phys. Chem. 77, 1129-1132. 15 East, E.J., Chang, R.C.C., Yu, N.-T. and Kuck, J.F.R. (1978) J. Biol. Chem. 253, 1436-1441. 16 Yu, N.-T., Jo, B.H. and OShea, D.C. (1973) Arch. Biochem. Biophys. 156, 71-76. 17 Siamwiza, M.N., Lord, R.C., Chen, M.C., Takamatsu, T., Harada, I., Matsuura, H. and Shimanouchi, T. (1975) Biochemistry 14, 4870-4876. 18 Yu, N.-T. (1974) J. Am. Chem. SOC.96, 4664-4668. 19 Craig, W.S. and Gaber, B.P. (1977) J. Am. Chem. SOC.99, 4130-4134. 20 Takesada, H., Nakanishi, M., Hirakawa, A.Y. and Tsuboi, M. (1976) Biopolymers 15, 1929-1938. 21 Ozaki, Y., Mizuno, A,, Itoh, K., Yoshiura, M., Iwamoto, T. and Iriyama, K. (1983) Biochemistry 22, 6254-6259. 22 Prescott, B., Sitaraman, K., Argos, P. and Thomas, G.J. (1985) Biochemistry 24, 1226-1231. 23 Johnson, C.R., Ludwig, M. and Asher, S.A. (1986) J. Am. Chem. SOC.108, 905-912. 24 (a) Dudik, J.M., Johnson, C.F. and Asher, S.A. (1985) J. Phys. Chem. 89, 3805-3814. (b) Mayne, L.C., Ziegler, L.D. and Hudson, B. (1985) J. Phys. Chem. 89, 3395-3398. 25 Rava, R.P. and Spiro, T.G. (1985) Biochemistry 24, 1861-1865. 26 Johnson, C.R., Ludwig, M., ODonnell, S. and Asher, S. (1984) J. Am. Chem. Soc. 106, 5008-5010. 27 Copeland, R.A., Dasgupta, S. and Spiro, T.G. (1985) J. Am. Chem. SOC.107, 3370-3371. 28 Copeland, R.A. and Spiro, T.G. (1985) Biochemistry 24, 4960-4968. 29 Lanir, A,, Yu, N.-T. and Felton, R.H. (1979) Biochemistry 18, 1656-1660. 30 Spiro, T.G. (1983) In: Iron Porphyrins, Part I1 (A.B.P. Lever and H.B. Gray, eds.), pp. 91-159, Adison-Wesley, Reading, Mass. 31 Matsukawa, S., Mawatari, K., Yoneyama, Y. and Kitagawa, T. (1985) J. Am. Chem. SOC. 107, 1108-1113.

62 32 Yu, N.-T., Benko, B., Kerr, E.A. and Gersonde, K. (1984) Proc. Natl. Acad. Sci. USA 81, 5106-5110. 33 Carey, P.R. and Schneider, H. (1978) Acc. Chem. Res. 11, 122-128. 34 Carey, P.R. (1982) Biochemical Applications of Raman and Resonance Raman Spectroscopies, Ch. 6. Academic Press, New York. 35 Carey, P.R. (1981) Can. J. Spectrosc. 26, 134-142. 36 Carey, P.R. and Storer, A.C. (1983) Acc. Chem. Res. 16, 455-460. 37 Carey, P.R. and Storer, A.C. (1984) AMU. Rev. Biophys. Bioeng. 13, 25-49. 38 Carey, P.R. and Storer, A.C. (1985) Pure Appl. Chem. 57, 225-234. 39 Benevides, J.M., Lemeur, D. and Thomas, G.J. (1984) Biopolymers 23, 1011-1024. 40 Verduin, B.J.M., Prescott, B. and Thomas, G.J. (1984) Biochemistry 23, 4301-4308. 41 Nishimura, Y., Tsuboi, M., Nakano, T., Higuchi, S., Sato, T., Shida, T., Uesugi, S., Ohtsuka, E. and Ikehara, M. (1983) Nucleic Acids Res. 11, 1579-1588. 42 Small, E.W. and Peticolas, W.L. (1971) Biopolymers 10, 1377-1416. 43 Lafleur, L., Rice, J. and Thomas, G.J. (1972) Biopolymers 11, 2423-2437. 44 Aylward, N.N. and Koenig, J.L. (1970) Macromolecules 3, 590-596. 45 Tomlinson, B.L. and Peticolas, W.L. (1970) J. Chem. Phys. 52, 2154-2156. 46 Morikawa, K., Tsuboi, M., Takahashi, S., Kyogoku, Y., Mitsui, Y., Iitaka, Y. and Thomas, G.J. (1973) Biopolymers 12, 799-816. 47 Shimanouchi, T., Tsuboi, M. and Kyogoku, Y. (1967) Adv. Chem. Phys. 7, 435. 48 Erfurth, S.C., Kiser, E.J. and Peticolas, W.L. (1972) Proc. Natl. Acad. Sci. USA 69, 938-941. 49 Brown, E.B. and Peticolas, W.L. (1975) Biopolymers 14, 1259-1271. 50 Thomas, G.J. (1975) Vib. Spectra Struct. 3, 239. 51 Prescott, B., Steinmetz, W. and Thomas, G.J. (1984) Biopolymers 23, 235-256. 52 (a) Thamann, T.J., Lord, R.C., Wang, A.H.J. and Rich, A. (1981) Nucleic Acids Res. 9, 5443-5457. (b) Benevides, J.M. and Thomas, G.J. (1983) Nucleic Acids Res. 11, 5747-5761. 53 Thomas, G.A. and Peticolas, W.L. (1983) J. Am. Chem. SOC.105, 993-996. 54 Blazej, D.C. and Peticolas, W.L. (1977) Proc. Natl. Acad. Sci. USA 74, 2639-2643. 55 Chinsky, L., JoUes, B., Laigle, A., Turpin, P.Y., Taboury, J. and Taillandier, E. (1984) Biopolymers 23, 1931-1942. 56 Nishimura, Y., Hirakawa, A.Y. and Tsuboi, M. (1978) Adv. Infrared Raman Spectrosc. 5, 217-275. 57 Kubasek, W.L., Hudson, B. and Peticolas, W.L. (1985) Proc. Natl. Acad. Sci. USA 82, 2369-2373. 58 Fodor, S.P.A., Rava, R.P., Hays, T.R. and Spiro, T.G. (1985) J. Am. Chem. Soc. 107, 1520-1529. 59 Chinsky, L., Turpin, P.Y., Duquesne, M. and Brahms, J. (1977) Biochem. Biophys. Res. Commun. 75, 766-771. 60 Nishimura, Y., Hirakawa, A.Y., Tsuboi, M. and Nishimura, S. (1976) Nature (London) 260, 173-174. 61 Verduin, B.J.M., Prescott, B. and Thomas, G.J. (1984) Biochemistry 23, 4301-4308. 62 Gaber, B.P. and Peticolas, W.L. (1977) Biochim. Biophys. Acta 465, 260-274. 63 Levin, I.W. (1984) Adv. Infrared Raman Spectrosc. 11, 1-48. 64 Mendelsohn, R., Sunder, S. and Bernstein, H.J. (1976) Biochim. Biophys. Acta 443, 613-617. 65 Bunow, M.R. and Levin, I.W. (1977) Biochim. Biophys. Acta 489, 191-206. 66 Gaber, B.P., Yager, P. and Peticolas, W.L. (1978) Biophys. J. 22, 191-207. 67 Bansil, R., Day, J., Meadows, M., Rice, D. and Oldfield, E. (1980) Biochemistry 19, 1938-1943. 68 Gaber, B.P., Yager, P. and Peticolas, W.L. (1978) Biophys. J. 24, 677-688. 69 Faiman, R., Larsson, K. and Long, D.A. (1976) J. Raman Spectrosc. 5, 3-7. 70 Lis, L.J., Kauffman, J.W. and Shriver, D.J. (1975) Biochim. Biophys. Acta 406, 453-464. 71 Lippert, J.L., Lindsay, R.M. and Schultz, R. (1980) Biochim. Biophys. Acta 599, 32-41. 72 Taraschi, T. and Mendelsohn, R. (1980) Proc. Natl. Acad. Sci. USA 77, 2362-2366. 73 Mendelsohn, R. and Taraschi, T. (1978) Biochemistry 17, 3944-3949. 74 Lavialle, F., Levin, I.W. and Mollay, C . (1980) Biochim. Biophys. Acta 600, 62-71. 75 Lippert, J.L., Gorczyca, L.E. and Meiklejohn, G. (1975) Biochim. Biophys. Acta 382, 51-57. 76 Verma, S.P. and Wallach, D.F.H. (1976) Biochim. Biophys. Acta 436, 307-318. 77 Verma, S.P. and Wallach, D.F.H. (1976) Proc. Natl. Acad. Sci. USA 73, 3558-3561. 78 Koyama, Y., Long, R.A., Martin, W.G. and Carey, P.R. (1979) Biochim. Biophys. Acta 548,153-160. 79 Bunow, M.R. and Levin, I.W. (1977) Biochim. Biophys. Acta 464, 202-216.

63 80 Koyama, Y., Carey, P.R., Long, R.A., Martin, W.G. and Schneider, H. (1979) J. Biol. Chem. 254, 10276-10285. 81 Yu, T.-T. and Jo, B.H. (1973) Arch. Biochem. Biophys. 156, 469-474. 82 Carey, P.R. (1983) Trends Analyt. Chem. 2, 275-277.

References for Table 2 a. Spiro, T.G. (1983) In: Iron Porphyrins, Part I1 (A.B.P. Lever and H. Grey, eds.) pp. 89-160, Addison-Wesley, Reading, Mass. b. Bangcharoenpaurpong, O., Schomacker, K.T. and Champion, P.M. (1984) J. Am. Chem. SOC.106, 5688-5698. c. Lutz, M. (1984) In: Advances in Infrared and Raman Spectroscopy (R.J.H. Clark and R.E. Hester, eds.) Vol. 11, pp. 260-266. Wiley, Chichester. d. Uno, T., Nishimura, Y., Makino, R., Iizuka, T., Ishimura, Y. and Tsuboi, M. (1985) J. Biol. Chem. 260, 2023-2026. e. Sitter, A.J., Reczek, C.M. and Terner, J. (1985) J. Biol. Chem. 260, 7515-7522. f. Ching, Y., Argade, P.V. and Rousseau, D.L. (1985) Biochemistry 24, 4938-4946. g. See text. h. Findsen, E.W., Scott, T.W., Chance, M.R. and Friedman, J.M. (1985) J. Am. Chem. Soc. 107, 3355-3357. Dasgupta, S., Spiro, T.G., Johnson, C.K., Dalickas, G.A. and Hochstrasse, R.M. (1985) Biochemistry 24, 5295-5297. i. Rousseau, D.L. and Ondrias, M.R. (1983) Annu. Rev. Biophys. Bioeng. 12, 357-380. j. Eyring, G., Curry, B., Broek, A,, Lugtenburg, J. and Mathies, R. (1982) Biochemistry, 21, 384-393. k. Smith, S.O., Myers, A.B., Pardoen, J.A., Winkel, C., Mulder, P.P.J., Lugtenburg, J. and Mathies, R. (1984) Proc. Natl. Acad. Sci. USA 81, 2055-2059. Hildebrandt, P. and Stockburger, M. (1984) Biochemistry 23, 5539-5548. 1. Maeda, A., Ogurusu, T., Yoshizawa, T. and Kitagawa, T. (1985) Biochemistry 24, 2517-2521. m. Carey, P.R. (1982) Biochemical Applications of Raman and Resonance Raman Spectroscopies, pp. 143-153. Academic Press, New York. n. Shiemke, A.K., Loehr, T.M. and Sanders-Loehr, J. (1984) J. Am. Chem. SOC.106, 4951-4956. 0. Sjoberg, B., Loehr, T.M. and Sanders-Loehr, J. (1982) Biochemistry 21, 96-102. p. Ozaki, Y., Nagayama, K., Kyogoku, Y., Hase, T. and Matsubara, H. (1983) FEBS Lett., 152, 236-240. Johnson, M.K., Czernuszewicz, R.S., Spiro, T.G., Fee, J.A. and Sweeney, W.V. (1983) J. Am. Chem. SOC.105, 6671-6678. q. Yachandra, V.K., Hare, J., Gewirth, A., Czernuszewicz, R.S., Kimura, T., Holm, R.H. and Spiro, T.G. (1983). J. Am. Chem. SOC.105, 6462-6468. r. Yachandra, V.K., Hare, J., Moura, I. and Spiro, T.G. (1983) J. Am. Chem. SOC.105, 6455-6461. s. Woodruff, W.H., Norton, K.A., Swanson, B.I. and Fry, H.A. (1984) Proc. Natl. Acad. Sci. USA 81, 1263-1267. t. Schmidt, J., Coudron, P., Thompson, A.W., Walters, K.L. and McFarland, J.T. (1983) Biochemistry 22, 76-84. u. Kitagawa, T., Nishina, Y., Kyogoku, Y., Yamano, T., Ohishi, N., Takai-Suzuki, A. and Yagi, K. (1979) Biochemistry 18, 1804-1808. v. Kitagawa, T., Nishina, Y., Shiga, K., Watari, H., Matsumura, Y. and Yamano, T. (1979) J. Am. Chem. Soc. 101, 3376-3378. x. Nishina, Y., Shiga, K., Miura, R., Tujo, H., Ohta, M., Miyaka, Y., Yamano, T. and Watari, H. (1983) J. Biochem. (Japan) 94,1979-1990. z. Sugiyama, T., Nisimoto, Y., Mason, H.S. and Loehr, T.M. (1985) Biochemistry 24, 3012-3019. aa. Ref. c. pp. 211-300. bb. Ref. m. pp. 125-133.

64 cc. Koyama, Y., Long, R.A., Martin, W.G. and Carey, P.R. (1979) Biochim. Biophys. Acta 548, 153-160. dd. Salares, V.R., Young, N.M., Bernstein, H.J. and Carey, P.R. (1977) Biochemistry 16, 4751-4756. ee. Wilbrandt, R. and Jensen, N.-H. (1983) In: Time Resolved Vibrational Spectroscopy (G.H. Atkinson, ed.), pp. 273-285, Academic Press, New York. ff. Margulies, L. and Toporowicz, M. (1984) J. Am. Chem. SOC.106, 7331-7336.

A. Neuberger and L.L.M. Van Deenen (Eds.) Modern Physical Methodr in Biochemistry, Part B 0 1988 Elsevier Science Publishers B.V. (Biomedical Division)

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CHAPTER 3

Rapid reaction methods in biochemistry QUENTIN H. GIBSON Department of Biochemistry, Molecular and Cell Biology, Cornell University, Ithaca, N Y 14853, U.S.A.

1. Introduction The idea of a rapid reaction is so much conditioned by experience and laboratory equipment as to be hard to define nowadays. When the first rapid reactions in biochemistry were studied by Hartridge and Roughton more than 60 years ago, a rapid reaction was simply one too fast to follow using a stopwatch to time removal of samples from a reaction vessel. A modern equivalent might define rapid as beyond the reach of the apparatus expected to be part of the equipment of an average biochemical laboratory, and translate into a half-time less than 5-10 sec. The choice of methods to discuss is even more difficult because little equipment has achieved off-the-shelf status, and groups of workers have assembled unique systems tailored to specific applications. The present material therefore represents an arbitrary selection, influenced by personal bias.

2. Continuous flow T h s was the first effective method used to follow a rapid biochemical reaction, and was developed by Hartridge and Roughton [l]in the Physiological Laboratory, Cambridge, England, immediately after World War I. Their work was so original, and the problems they met and overcame are so relevant to any biological application of rapid kinetic methods today as to merit discussion. During the first decade of the present century the major factors influencing the position and form of the oxygen equilibrium curve of mammalian hemoglobin were established, primarily by Barcroft and his associates, at Cambridge. It was natural to ask if these in vitro curves really applied in the living animal, and time became a critical consideration since the mammalian red cell was known to spend only about one second in the capillaries of the lung and tissues. A preliminary attempt to measure the rate of deoxygenation of hemoglobin by bubbling nitrogen gas through a solution is described in the first edition of ‘The Respiratory Function of the Blood’ [2] whch

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appeared in 1914. By the end of the war, however, Barcroft realized that the experiment was really measuring the rate of diffusion from the solution to the gas bubbles, and a new attack was set in motion. In the method which worked, two large earthenware bottles each of about 40 1 capacity, were filled with a buffer equilibrated with a known partial pressure of oxygen, and with a solution of deoxyhemoglobin. The solutions were driven by nitrogen pressure through a brass mixing chamber with eight tangentially arranged jets, four for each solution. This was estimated to have a half-time for mixing of 0.3 msec, and was made by Hartridge on a lathe in his garage. It was a sophisticated and complex design, and its performance has not been materially improved upon since. The mixture flowed into a tube of 1 cm diameter, and because the flow was turbulent there was little radial distribution of velocities across it, or, in other words, the mixture traveled down the tube as if in blocks. The age of a block at a given distance from the mixer was (volume from mixer to point of observation)/flow rate. To determine the rate of reaction the composition of the mixture at the point of observation was also required. The method employed was a visual optical one in which the 6 nm difference in the position of the alpha-bands of oxy- and carbon monoxyhemoglobins was used, with a calibration curve, to measure the amount of oxyhemoglobin formed at the point of observation. This method was entirely specific to hemoglobin, and by Indsight, it might have been better to use a visual polarization spectrophotometer such as the Koenig-Martens instrument, although I know of no evidence that the Cambridge laboratory ever had one. However that may be, a skilled observer could set the position of the bands in the Hartridge instrument in about 15 sec, with solutions strong enough to show a clear alpha band. The requirements of the spectroscope determined almost everything about the experiment. It could be set about 5 mm from the mixer, giving a least time of observation of 1 msec with a flow rate of 0.5 l/sec and a fluid consumption of 7 1 per point. The rate of flow was measured by timing the flow period with a stopwatch and collecting the effluent in a large bucket for later measurement. T h s first apparatus gave substantially correct results, and, at a single step, extended the time scale for solution measurements by 5 orders of magnitude, an achevement rare in any field of science. The original apparatus did not undergo any worthwhile development largely because the measurement of band positions restricted the reactions which could be followed to a handful of hemoglobin reactions, and the fluid and concentration requirements were beyond the capacity of preparative biochemistry of the time. The principle of the apparatus was maintained in a series of new designs, primarily due to Millikan [3], whxh used photovoltaic cells, introduced about 1930, and shortperiod mirror galvanometers with a period of a second or so to reduce the fluid requirements. The 1cm observation tube was reduced to 1 mm in diameter, and the mixer was built into the interior of a three-way stopcock. The reagents were contained in syringes of 10 to 20 ml capacity, and three different time points measured in each kinetic run by using a constant-speed motor to wind the driving wire on a three-step drum. The 1000-fold economy in volume and 10-fold reduction in concentration allowed Millikan to study myoglobin, then recently isolated by

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Theorell [4], and hernocyanin. The rate of the oxygen-myoglobin reaction of 2 X 107/msec was accurately determined, a reaction as fast as any which has been studied by flow-mixing methods. This line of work came to an end with Millikan’s untimely death in a climbing accident, and his apparatus has never been replicated, although it was preserved for many years in Roughton’s laboratory. The final steps in fluid economy in a continuous-flow apparatus were taken in 1941 when Chance [5] described his accelerated-flow apparatus. The photovoltaic cell-galvanometer combination was replaced by a vacuum photocell, d.c. amplifier, and cathode ray oscillograph, and, instead of establishing and maintaining a fixed rate of flow, the varying rate of movement of the reagent syringes was registered with a linear potentiometer differentiator, and amplifier circuitry, on a second channel in the oscillograph. The fluid requirement was reduced by all these changes to 0.1 ml, although perhaps with some loss in performance as compared with Millikan’s apparatus. The maximum rate of flow was probably less, and the precision of the results may not have been so great. With this apparatus, rapid reaction methods may be said to have entered biochemistry proper, and Chance used the equipment in his classic work on enzyme-substrate complexes calling only for quantities of enzyme well within the range accessible to standard preparative methods. Even this more useful apparatus was scarcely duplicated, this time because the techniques it incorporated were beyond the reach of the average biochemical worker, and were, in fact, well in advance of their time. T h s was particularly true of the signal amplification systems which contained vacuum tube d.c. amplifiers, devices with especially severe problems. Chance developed modular amplifiers, again ahead of the practice of the time, and also stabilized the tungsten light source, a troublesome matter before solid-state devices. At present there is no general-purpose continuous-flow apparatus suitable for biochemical work, although there are a number of specialized applications in whch continuous flow has been used. These are often required when optical monitoring of the reaction is not possible. There is no obvious limit to the combinations of flow apparatus with monitoring methods, and the continuous-flow method lends itself particularly to batch procedures. An example is offered by flow-quench methods [6]. In these the output from a mixer is aged by passage down a fixed length of observation tube and is then mixed with an excess of a third reagent whch stops the reaction, either using a second mixer, or, more simply, directing the outflow from the observation tube into a beaker or tube of quench reagent. The whole sample is then analyzed chemically yielding one point on a kinetic progress curve, and the procedure repeated with a different length of observation tube. The whole procedure is quite tedious and the possible errors more serious than with optical observation. Furthermore, the practical time range that can be covered is quite limited because of the amount of liquid required to fill a long observation tube (in this application usually called the intermediate volume). Matters can be helped along by using slower rates of flow, but the rate must be great enough to maintain turbulence, at the very least at the mixer. In addition, the intermediate volume must be washed out and perhaps dried between points. Although there have been biochemical applications, they are relatively few.

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A related procedure is in observation by electron paramagnetic resonance spectroscopy. As this is important in biochemistry, considerable effort and attention has been given to the method, but it is far from being a routine procedure. The general principle [7] is similar to the quench procedure just mentioned, but instead of stopping the reaction with an excess of chemical reagent, it is slowed by cooling suddenly. Unfortunately, this is far from easy, and highly specialized apparatus has been used. In one form a large hydraulic ram was driven at a constant speed by a powerful electric motor, forcing fluid from syringes through a mixer, and through a fine jet needed to break it into the small droplets essential for rapid cooling. The mixer and jets were constructed from polyethylene tubing which may have saved the syringes from destruction, but at the price of uncertainty about jet diameter. The spray from the jet has usually been cooled by mixing with pentane cooled to CO, temperatures. The fine ice crystals were formed in a broad tube with an e.p.r. tube fused to its end, allowing the crystals to be tamped down with a perforated plastic plate mounted on a stalk. This operation is more easily described than performed, especially if the ice crystals are as small as they should be. In spite of these difficulties successful use of the method has been reported by several laboratories, but careful controls and individual investigation of each case remain mandatory. Continuous-flow methods allow use of a response time of the recording system longer than the life of the reaction to be followed. As an example, most electrodes have response times of the order of seconds. If they are built into a flow system the time determined by its dimensions and rate of flow will be substituted for the response of the electrode. The analogy with the use of the Hartridge spectroscope is obvious. There have been relatively few applications of the principle. As pointed out in the preceding paragraph the recording equipment used for a continuous flow experiment may be simpler and slower in response than that required by relaxation methods operating in real time. As a result, if it is necessary to make a few kinetic measurements, and if the supply of material will permit, it may be much cheaper to set up an unambitious flow apparatus than to attempt other procedures. A continuous flow method which seems to have disappeared almost without trace is the thermal method developed by Roughton [8]. In its most effective form a thermopile in the form of a needle several inches long was suspended in the observation tube. The temperature difference between the ends of the needle depended on the heat of the reaction being examined, on its rate, and on the concentration of the reagents. The difficulty is that relatively few reactions are associated with large enough heat changes to allow second-order reactions to be followed in the time range accessible to flow methods. This is unfortunate, incurable, and has led to the disuse of the method which has the advantage of measuring a very important characteristic of a reaction in an unusually direct way. It seems that most of the potential of the continuous-flow methods has already been realized. One limitation arises from the mixing process itself. If two liquids are to be mixed rapidly they must be broken up into tiny packets moving fast. They will be slowed by viscosity, and the smaller the packets, the more effective viscosity will be. The effect is that more work must be done on the liquids both to break them up

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and to keep the mixture in motion. This work largely appears as heat in the solution. With the pressures used in a common stopped-flow apparatus the rise in temperature is 0.2" C. To drive the liquids through 10 times faster would call for a 100-fold increase in pressure, and produce a temperature jump of 20 " C. There is certainly some hope of increasing mixing efficiency since in the usual designs work is expended alike on liquids which have not mixed and on portions of fluid in which mixing is already largely complete, but it is hard to guess how much room for improvement remains or whether radically different designs such as infinite-jet mixers will perform as expected. It is perhaps discouraging that the very first apparatus to be built by Hartridge and Roughton had at least the same performance in terms of speed as the most modem designs, although in all other respects, there can be no comparison.

3. Stopped flow The late F.J.W. Roughton used sometimes to claim that he and Hartridge had invented stopped-flow procedures because, when they wished to follow very slow reactions they clipped off the rubber tubing connecting their large storage bottles to the observation tube and took spectroscope readings on the stationary mixture at appropriate intervals thereafter. More practically, Chance [ 5 ]observed that when an accelerated flow measurement had been completed, and after random motions in the observation tube had ceased in about 0.1 sec, any remaining reaction might be followed in real time with the oscillograph. The motion of the spot on the x-axis was provided by the time base, and the y-deflection followed the progress of the reaction. The dead period during deceleration of flow arose because as flow ceased to be turbulent mixing became slow and inefficient, and swirls of unmixed reagents crossed the observation point, which was, of course, set as close as possible to the mixing chamber. It remained for Gibson and Roughton [9] to point out that if flow were stopped suddenly rather than gradually, real time observation on properly mixed fluid might be made to cover the time range from 2 msec or so for as long as needed. It is probably not unfair to call all the apparatus so far described quirky and difficult to use, indeed, the designer, constructor and only effective user were often the same person. A serious attempt to develop a robust and simple stopped-flow apparatus was made by Gibson and Milnes [lo], and in the end some 500 or so examples were manufactured. A detailed description of its construction and use has been given by Gibson [ll],and little significant alteration to the mechanical flow unit has since been made. Anyone seriously thinking of using or building a stopped-flow apparatus should probably consult these references, old though they are. There are some indications that a new generation of stopped-flow apparatus may appear shortly, and, because of the relative complexity and expense of the old designs, they are likely to deserve close consideration. Although the flow unit has changed little, data recording and storage have been transformed by the appearance first, of the minicomputer, and more recently of the

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microcomputer. At first, a photograph of the oscilloscope trace was taken, and, before storage screens, the success or failure of the operation became apparent upon development of the film. With the storage oscilloscope a frame could be assembled on the screen before photography, but in both cases the photograph had to be handled manually thereafter, measuring the trace or an enlarged projection, and converting the readings to absorbance if the change measured exceeded some 0.05 or so. A dubious improvement may be made by using a logarithmic amplifier to reduce the values to absorbance automatically. The difficulty is that such an amplifier requires a reference voltage corresponding to 100%reaction. This can only come from the spent solution remaining in the observation tube from the previous operation of the apparatus. This baseline position is typically not very stable because successive shots do not produce exactly the same mixture of reagents. The output of the amplifier then contains an offset which may be quite misleading. Computer-assisted data collection is much more satisfactory, is cheaper than it was, and is likely to become increasingly accessible. The system used for the computer can only be designed around the hardware actually available, but with the multiplicity of cards available for the major brands of microcomputer, interfacing can now be carried out with a minimal knowledge of the actual workings of the computer. A stopped-flow apparatus is a comparatively slow speed device, and data may be transferred directly to memory without using an intermediate transient recorder. The actual operation of a/d conversion and storage will usually call for an assembly language subroutine, and subsequent averaging and processing should be carried on using an efficient compiled higher level language, not interpretative Basic. The very ease of operation of a computerized data acquisition system can present problems because of the sheer bulk of information collected, much of whch may never be properly digested. It is desirable, therefore, to begin condensation as early in the process as possible. If, say, 1024 points are collected to represent a kinetic run, these should be smoothed and reduced to 20 or so before storage, and replicate runs may conveniently be averaged at the time of collection. The program should attach the date, conditions, and as much general information as possible to each unit of data stored. Much of this information will be repetitive, but is invaluable later an. It should be possible to modify the header for each run without re-entering it. At the moment, floppy disks are the most economical and convenient storage medium. It is probably better to avoid the use of the operating system directory which may limit the numbers of data sets which can be stored and expose them to the risk of total loss should the directory be damaged. It may be useful to summarize the approximate performance to be expected from an optical stopped-flow apparatus. The highest first-order rate is of the order of 500/sec, the highest second-order rate depends on the extinction coefficient of the reactant and on whether the reaction is rapidly reversible. In the best case with a large absorbance change of, say, 50/mM, with a 2 cm observation tube and an irreversible reaction, a rate of 5 X 108/Msec could be measured. Absorbance changes may be measured with a reproducibility of perhaps 2% if the change exceeds 0.03; the figure depends on the total absorbance of the solutions, and much smaller changes may be measured if the half time is longer than 0.2 sec. Using an

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f/4 monochromator and a quartz-iodine lamp, photon noise is seldom a problem at wavelengths above 350 nm up to the red limit of the multiplier in use. 3.1. Miscellaneous stopped-flow devices

Many obvious extensions have been made. Fluorescence observation is often useful, but calls for a properly designed cuvette. If at all possible, the whole apparatus should be designed with a view to fluorescence work; some commercial attachments to plug into absorbance instruments are more ingenious than practical. Equipment has been constructed to permit a temperature jump experiment to be performed on a mixture generated in the cuvette by the flow apparatus. The difficulties in evaluating the results of such an experiment are so great as to be almost prohibitive. Several types of equipment with multiple mixers allowing more than two reagents to be mixed in sequence are available. These differ from flow-quenchmg instruments by providing optical monitoring of the final mixture. There are cases where t h s facility could be applied. Fluorescence polarization has been examined in stoppedflow experiments. The combination of properties required of a useful system is such that few, if any, exist. The fluorophore must have a high quantum yield and a high limiting polarization. It must continue to fluoresce when bound to a protein, and must bind with a sufficiently small dissociation constant so that a high proportion is effectively immobilized. Finally, a reaction in the stopped-flow time range must take place in the system. Limited application of conductivity measurements has been made. The cell forms part of an a.c. bridge and the out-of-balance voltage is amplified, rectified, and displayed. Low radio frequencies of the order of 100 kHz have been used. It has been implicitly assumed that observations at a single wavelength are to be made using non-scattering solutions. In non-scattering solutions it is often valuable to have observations at several wavelengths. Obviously, this may be done by resetting the monochromator and repeating the run. The possibility of scanning a spectrum in conjunction with the operation of a stopped-flow apparatus is interesting here. The oldest method is to move an element in the monochromator so as to scan a defined wavelength range repeatedly, often at line frequency. During each scan the absorbance at, say, 100 wavelengths is recorded. In its most ambitious form, carrying on true split-beam spectrophotometry, the output from a second channel must be recorded also to provide the baseline voltage. T h s has been done by using a second mirror oscillating at a much higher frequency, and might alternatively be done using fiber optics and two detectors. As an alternative to oscillating a mirror, a high speed rotor with several mirrors mounted on it has been used to the same end. In both cases, the detector continues to be a photomultiplier as usual. It is now possible to obtain arrays of photodiodes in a variety of shapes. If such an array, made up of 100 parallel strips, were placed in the focal plane of a monochromator, ‘replacing and extending the exit slit, a range of wavelengths could be recorded simultaneously. At present, these solid-state devices are much less sensitive than photomultipliers. The multiplier, however, is a mature device, while solid-state devices, either photodiodes or charge coupled are developing rapidly.

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Even if the hardware were available, it is not certain that much would be gained from a multiwavelength system. To obtain useful readings at a range of wavelengths, the concentration of reagents would have to be two to three times greater than is needed at an optimum in the difference spectrum. Furthermore, the noise level in the data is virtually certain to be higher in the scanned spectrum, because of mechanical imperfections, electrical noise or both. In using the stopped-flow apparatus, a definite volume is unavoidably wasted to wash out the dead space and to establish a uniform concentration in the syringes. T h s volume is independent of concentration. The loss would be proportionately higher for the smaller volume of more concentrated solution. Finally, the outflow of data should not be underestimated. Even in a single beam mode it would be necessary to acquire and store 12000 data values per second. This is not impossible, but is not trivial either. It is likely that more data would be acquired altogether - who, after all is going to make 100 separate stopped flow runs on the same solution? - but the price would be high in terms both of hardware and software. 3.2. Relaxation methods

As with flow methods, the principle of the most important of these, flash photolysis, is due to Hartridge and Roughton. At the time their work started they intended to study the reaction of carbon monoxide with hemoglobin using the photosensitivity first observed by Haldane and Lorrain Smith at the end of the 19th century. In their apparatus a stream of carbon monoxyhemoglobin flowed in succession past a bright photodissociating light and then through an observing beam falling on the reversion spectroscope. The liquid was made to flow through the tube, but no effect could be seen. Control experiments showed that the brightest light available to them, an image of the crater of a d.c. carbon arc, simply did not produce significant photodissociation, in terms of their observing system. The photosensitivity of carbon monoxyhemoglobin originally showed up as a change in the partition of hemoglobin between oxygen and carbon monoxide on illumination of dilute solutions. Hartridge and Roughton therefore tried their experiment with both ligands present, and the equilibrium was displaced. As in the flow experiment, the rate of the return to the dark equilibrium was measured by the distance between the point of illumination and the point of observation. They also performed a number of experiments with a closer formal resemblance to a modem relaxation experiment when they placed a cell filled with carbon monoxyhemoglobin in equilibrium with both oxygen and carbon monoxide in a box with a shutter. In the open position the shutter admitted light from the arc lamp. At right angles, a second light beam passed through the cell to fall on the reversion spectroscope. The reversion spectroscope was set to a predetermined wavelength, and the shutter left open for several seconds. As the shutter was closed, a stopwatch was started while the observer followed the movement of the absorption bands in the spectroscopk. Then, when the selected wavelength had been reached, the watch was stopped. The experiment was repeated appropriately, building up a kinetic curve for the return of the system to its dark equilibrium. Although the work had no practical influence whatever on later

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developments, this is the principle of relaxation experiments. Their initial failure and later success illustrate the principles involved quite clearly. One must have a light with a rate of work significantly exceeding the rate of return of the system to its dark state. It must be turned off sharply, otherwise the system will follow the light intensity downwards rater than relaxing at a rate determined by the chemistry of the system, and the observing system usually must have a time constant significantly shorter than the most rapid relaxation of the system. These principles were put into practice some 30 years latter by Porter and Norrish, who, however, were physical chemists, not biochemists. The early work was therefore directed to chemical ends, particularly the study of the triplet state - for which they shared the Nobel prize. There is a serious difficulty in all attempts to describe flash photolysis apparatus and experiments. It is that no single design of apparatus has ever been replicated in many laboratories. Rather, each group of experimenters have evolved their own equipment, tailoring its characteristics to suit the system under study. For the sake of concreteness, the properties of some of the principal elements of practical flash photolysis systems will be discussed, bearing in mind that cost is a meaningful laboratory parameter. 3.2.1. Flash sources If it can be used, there is simply no competitor for the photographc flash. It is cheap, long lived, reproducible, and controllable. The drawbacks are limited brightness, a broad spectrum which cannot be changed, and a shape of source ill-suited to illuminating a small area in a photocell. An effective rate of work based on carbon monoxide myoglobin, in a cell, may be 10000/sec or so. The cut-off of a thyristor controlled unit occurs in a few microseconds, quite short enough to allow the performance associated with a rate of photodissociation of 10000/sec to be fully used. The figure quoted is for a flash unit coupled to the cell with a tapered lucite light guide which allows the brightness at the cell to approach the brightness at the surface of the flashlamp. A convenient cell dimension is of the order of 1 cm2, with the observing and photolysis beams at right angles. This is appropriate in many biochemical applications where very great dilutions and long pathlengths are unsuitable because of protein adsorption on the cell surfaces, and because of possible dissociation of larger molecules into subunits. The xenon-filled tubes give white light. It follows that the flash will emit significantly at the wavelength of observation, and scattered light will prevent any observation until the light has died away. There is the further problem that the light does not go out completely when the flash is turned off, but continues at a low level, say 1% of peak intensity, for several milliseconds afterwards. This is due to effects such as phosphorescence of the material of the tubes, and cannot easily be altered. In addition, the observing photocell is likely to be blinded by the flash, delaying the time of first observation until it has recovered. In favorable cases, this problem can be solved by interposing complementary glass filters between the flash tube and light guide and in front of the photocell. If a monochromator is used, it should usually be placed between the sample cell and the photocell rather than between the observing light source and the

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sample cell. Furthermore, the observing beam should be made as bright as the sample will permit, since scattering artifacts depend on the ratio of the flash and observing intensities. The use of complementary filters cuts down the available light seriously, but, except for very slow reactions, is highly recommended. When choosing filters, it is almost always best to use a flashlamp filter transparent at long wavelengths. In the nature of things, these cut-off filters have better characteristics than band-pass filters, and fluorescence cannot be generated at the wavelength of observation. If it is available, an interference filter is ideal for use in the observing beam. Certain liquid filters have excellent characteristics, but are inconvenient in use. The remaining problem is that the trigger transformer used to ionize the gas of the flashlamp usually generates severe radio frequency interference. Screening and patient rearrangement of components offers the only remedy. The main capacitor discharge of the flash itself is associated with magnetic effects which may disturb a photomultiplier, again, placement and screening must be studied. A flexible fiber lightguide may be useful to let the observation system be set up further from the flash tube. Present-day photographic flash units work at a few hundred volts, and deliver 100 J in 3 to 5 msec or thereabouts. Older flash units operated at 2 to 5 kV to deliver the same energy in 0.2 msec. With specialty lamps operating at 20 kV the same total energy is available in 0.02 msec. In spite of the high rate of work, these h g h voltage units are probably best avoided, primarily because they have not had thyristor control. Although the flash is much brighter, it is not possible to follow correspondingly faster reactions, even with complementary filters. The chemical system is held away from equilibrium by the tail of the flash, and with a 2 kV flash the first undisturbed observation may not be possible until 1.5 msec or so after the flash is fired. The very high voltage systems are correspondingly expensive, flashlamp life is short, lamp form is unsuitable, and a laser may offer a better solution to the problem. At first sight it would seem that if high voltage flash discharge lamps are to be avoided; the two commonest types of laboratory laser, the dye laser and the neodymium glass or ruby lasers, which are pumped by high voltage flashlamps, should equally be shunned. There is something in this point of view, particularly with regard to dye lasers which require very high pumping voltages for good efficiency. Furthermore, lasers require at least a small measure of knowledge and experience for satisfactory operation. They have, however, countervailing advantages unmatched by any other light source. First, the light pulse is always short, for a dye laser typically 300 nsec, for a Q-switched solid-state laser 30 nsec. Secondly, the light is either monochromatic or confined to a relatively narrow band. Last, but far from least, because it is in a near parallel beam, it can be delivered where it is wanted to give a very high rate of work of l/nsec or better. Unlike the flashlamp with its afterglow, lasing action ends in a steeper-than-exponential manner, and scattered light is easily excluded from the observing system. One grave difficulty remains: a ruby laser gives red light, and neodymium glass near infra-red (1060 nm) light. Few materials of biochemical interest absorb at these wavelengths, so light from these lasers must be frequency doubled, giving near ultra-violet and green

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light, respectively, with the loss of most (say 80 to 90% or so) of the incident energy. Dye lasers give quite a choice of wavelengths, but as the wavelength is shortened output falls and the flashlamp must be driven harder and harder. Optimum output is obtained in the green to orange region of the visible spectrum. Even the best dyes have problems, and a limited life, while output varies continuously during the life of the dye. Excimer lasers are more expensive, at present, than dye or solid-state lasers. They deliver light in the ultra-violet at wavelengths depending on the gas filling (e.g. XeCl at 308 nm) with a pulse length of 20 nsec, and energies up to 1 J or more. There is a variety of designs on the market, none intended for the academic biochemistry laboratory, but the combination of high power, wavelength range, and short pulse length makes the field worth watching. In addition to the lasers so far discussed, there is a major range of devices intended to give shorter pulses, down to a few picoseconds. Although these lasers have been applied in biochemistry, in the study of heme proteins and in photosynthesis, their operation calls for special skills and experience, and cannot be discussed further. 3.2.2. Observation light sources The choice of observing sources is relatively simple, and depends on the nature of the photolysis source. If the photolysis source is a flashlamp which can irradiate a large volume of solution, then a tungsten-halogen lamp should be used. The observing beam should be spread out over the illuminated volume to minimize possible photochemical effects. If a laser is used, there will be only a small illuminated volume. The observing beam must come from a compact source so that its image at the cell may fall within the volume illuminated by the laser. The requirement is met by the Xe arc. It is best to use a small (say 75 W) arc whch moves less than high-powered arcs. There will be a considerable photochemical effect in the cell and, if possible, an interference filter should be used between it and the lamp. If observation is to be extended to the nanosecond range, the rate of delivery of quanta from a normal arc is too low to permit a reasonable signal/noise ratio. The arc may then be pulsed to, say, 20 times normal brightness for, say 0.1 msec, firing the photolysis flash, say 0.01 msec, after the lamp pulse begins. The extra brightness of the observing beam will not have time enough to produce significant photochemical effects at the cell. This procedure does not seem to shorten the life of the Xe arc. A particularly attractive scheme for making simultaneous observations at several wavelengths has been reported from Eaton’s laboratory [13]. The observation beam is substituted by a pulse of fluorescence excited by a frequency doubled Nd laser, lasting for 10 nsec. After passing through the sample, the light is dispersed in a monochromator with a charge-coupled device (Vidicon) in the plane of the slit which accumulates information for a number of wavelengths. A kinetic curve is built up by repeating the experiment a number of times with different delays between the photolysis and observation laser pulses. 3.2.3. Light detectors A photomultiplier is almost always the device of choice. As there is usually plenty of light in the observing beam, the main precaution required is to observe the

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manufacturer’s recommendations on dynode voltage. Special circuits are required in the nanosecond region because the large dynode currents cannot be drawn from a conventional resistor chain, which must be supplemented by capacitors. Other problems arise in this range, perhaps because of space charge effects on dynode current, and linearity of the multiplier should be examined under operating conditions. A response time constant of about 2 nsec is accessible with conventional components working directly into 50 ohms. The comments made when discussing stopped-flow apparatus are applicable to flash photolysis, except at the highest speeds.

4. Combinations of flash photolysis with other techniques Flash photolysis by itself is of limited biochemical application because there are few systems to which it can be applied. The requirement for reversibility is particularly restrictive and prevents the direct study of say, cytochrome oxidase. If, however, one mixes carbon monoxide cytochrome oxidase with an oxygen-containing solution in a stopped-flow apparatus, the rapid reaction of oxygen with the enzyme is inhibited until the carbon monoxide is removed by a photolysis flash. This allows a reaction which is much too fast for direct stopped-flow observation (dead-time 2 msec) to be followed with an effective dead time of 1 psec, using a laser, or 5 psec using a conventional flash. In this case, the long photolysis flash does not limit observation because the flash can only remove carbon monoxide and the reaction with oxygen can occur during it. Just the same principle may be used to deal with ligands with apparent quantum yields beyond the range of the flash apparatus. For example, nitric oxide cannot by removed from hemoglobin using a photographic flash. If, however, carbon monoxyhemoglobin is mixed with nitric oxide in a flow apparatus and then flashed, the nitric oxide reaction is readily observed.

5. Temperature jump In this procedure, due to Manfred Eigen, a system at equilibrium is perturbed by a sudden change in temperature, typically induced by ohmic heating from a capacitor discharge. The reaction is followed as the system adjusts (relaxes) to the new equilibrium at the higher temperature. The application of the method is very restricted because the reaction must not only be reversible, but at equilibrium within the cell there must be an appreciable population of more than one species. In addition, with practical temperature jumps of a few degrees, it is rarely possible to displace the equilibrium far. The signal/noise ratio is correspondingly poor. Finally, all equilibria of the system are perturbed at the same time. Although this may be regarded as an advantage, since the relaxation spectrum is obtained, interpretation of the results is seriously complicated, and, except in the simplest cases, may be impossible. The time range is determined by the heating time constant on the one hand, and by the cooling of the cell, appreciable after some 250 msec, on the other.

The apparatus has been highly developed into a relatively standard form. An extensive review has been given by Eigen and De Mayer [12]. The most characteristic item of the apparatus is the cell. In one form, a cylinder of lucite is bored out at right angles to its long axis to receive two silica windows 1/4 in. thick about 1/2 in. apart. The round windows are held against plastic gaskets by threaded collars, and form two sides of the cell. The floor of the cell is formed by a gold- or platinum-plated electrode whose lower end forms a collar into whch the hgh voltage terminal of the discharge capacitor fits. The ground electrode forms the top of the cell and is attached to an external metal plate making good thermal contact with a bath maintained at the initial temperature. The experiment is performed by charging the capacitor to the required voltage and shorting it across the cell when it discharges with time constant RC. The value of R is about 100 ohms, and with C typically 50 n F charged to 25 kV, a rise of temperature of 2" C is 90% complete in 0.01 msec. There is no electrical disturbance other than the discharge of the heating capacitor. The heating time falls off as the square of the voltage, but values much above 30 kV are not commonly used. With very high voltages the current distribution in the cell becomes non-uniform, and the charge may not be applied to ohmic heating. The resistance quoted is for a strong electrolyte in 0.1 M solution: solutions of low ionic strength cannot be used. Observation is usually of absorbance change, and as the change is often only a few thousandths of an absorbance unit, the observing light beam is split to give first-order compensation for fluctuations in the source. A bright observing beam is essential to permit a reasonably short time constant, and a xenon arc is used. Fluorescence observation has been described, but is likely to be effective only with relatively slow reactions because of the difficulty of transferring sufficient quanta to the detector from an isotropic source at some distance. In principle, other methods of recording could be used, but because of the small signals, are unlikely to give good results. The main biological application of the temperature jump has been to heme proteins, especially hemoglobin where a full set of rates and amplitudes for human hemoglobin at pH 7 has been published by Ilgenfritz and Schuster [14]. In complex systems which have been fully studied by other means, the temperature jump procedure, which does, after all involve a very fundamental parameter, may be of value as an overall check of the system as a whole.

6. Miscellaneous methods 6.I . Time resolved resonance Raman spectroscopy

Static resonance Raman spectroscopy has emerged as an important and powerful method for investigating details of structure in compounds with strong absorption bands, such as hemoglobin (see, for example Asher [15]), and these advantages have been extended to kinetic studies by Dr. T.G. Spiro of Princeton, and Dr. J.M. Friedman of Bell Laboratories. It seems unlikely at present that their methods will

78

come into everyday use in biochemistry because of their cost and complexity, as well as some limitation in the systems which can be studied. The method is able to give information about bond lengths with high sensitivity and time resolution down to the subnanosecond region. As the major task of interpreting the spectra proceeds, a very detailed picture of movements of residues in the region of the heme may be expected. The area is currently in rapid development, and the interested reader is advised to examine the original literature. 6.2. Competitive methods

It is sometimes possible to use competition between a known and an unknown process to make an indirect kinetic measurement. A very simple example is the use of a photolysis flash not to produce a relaxation but to set up an approximation to a steady state. Then, if the system can be calibrated by reference to a known reaction, rates limited by the brightness of the flash rather than the response time of the recording system may be measured. There is, of course, a price to be paid for the gain of 2 to 3 orders of magnitude in time range. It is the need to use a model to evaluate the results. In the case discussed, one must know the quantum yield, or assume it, to work out the rate of the process competing with photodissociation by the photolysis light. The example given is formally similar to using a fluorescent dye of known lifetime to measure the rate of collisional quenching by iodide, and then measuring lifetime of several dyes by studying quenching. The result will not always be correct, however. The principle has been applied to show that oxygen has free access to tryptophan in several proteins, and to measure the rate of access of oxygen to the heme site in porphyrin globin. In this case the arrival of oxygen was followed by observing the disappearance of triplet absorbance following flash illumination of the sample. There are, of course, many possibilities of this general kind, usually very highly system-specific.

7. Data reduction Although the collection of data looms larger in the investigator’s eye, data reduction is commonly more time consuming and often more difficult. The first step should usually be to reduce the number of data points in a kinetic record to between 20 and 50. Otherwise, an excessive number of arithmetic operations will be required in later treatment. Now that logarithms may be calculated very quickly by coprocessors, one may assume that short segments of a plot of In(reactant) vs. time are likely to be linear - and, of course, in the case of a first-order reaction will be exactly so. The procedure is to take logarithms of the amount of reactant remaining at each time interval and fit a straight line to the required numbers of groups. The parameters can then be used to calculate the smoothed values for each time interval. This has the advantage over straightforward averaging that a value is available for zero time, again convenient in later data processing. An alternative is to fit a second-degree curve directly to the data points and again use the parameters to derive smoothed

79

values. In many practical cases, data sets may be approximated closely by sums of exponentials, but using this for smoothing purposes is questionable since it almost amounts to representing the data by a model and might seriously prejudice later curve-fitting operations. If varied time intervals have been used in the immediate process of data acquisition, it is appropriate to reduce the number of different time intervals used to 1 or 2. Occasionally it is suggested that data points be taken at geometrically related time intervals, and this has some merit when the data represent multiple processes with widely differing rates. On the other hand, transient recorders with the facility for collecting points in this way are not widely available, and the subsequent handling of the data is often less convenient. There is much to be said for preparing an analog data plot at an early stage in data treatment, and even for plotting by hand. The advantage is that a graph can present information in a more telling way than any list of numbers, and that plotting by hand compels closer inspection. A great deal of ingenuity has been applied to the problem of linearizing data, because deviations from a line are more easily recognized by eye than deviations from a curve. Inevitably, the price of linearization is a redistribution of weights, and sometimes a loss of intuitive feel for the significance of deviations. Well-known examples are the use of reciprocal plots in presenting enzyme kinetic data, and semi-logarithmic plots in presenting many kinetic time courses. In both cases, the data may be misrepresented, and especially so in the semi-logarithmic case. As the experimental curve approaches the baseline the apparent noise increases, and the curvature of the plot depends critically on knowing exactly where the baseline is. It is for this reason that the use of logarithmic amplifiers, which have been made available commercially in kinetic equipment, is best avoided, and especially so when using stopped-flow apparatus. With an amplifier, the baseline level must be known before the data are collected, and as each new mixture portion is a little different from the one which went before, the possibilities of trouble are obvious. In biochemical systems, in practice, heterogeneity is the rule rather than the exception, and it is a rare reaction which can be followed confidently and meaningfully beyond about 90-95%. Correspondingly, semi-logarithmic plots should not require more than 2-cycle paper. Data collected at logarithmic time intervals lend themselves to log-log plots. In such a plot, a single exponential process becomes an s-shaped curve, and multiple exponentials each generate an s of the same form appropriately displaced along the abscissa. If very widely different rates must be compactly represented, this plot is unrivaled, but it has little else to recommend it as interpretation requires either close attention, or else long familiarity with the method. The results of preliminary examination, and the object for whch the experiments were performed, dictate the later steps. If a first-order rate constant is all that is needed, the slope a of semi-log plot is enough for most purposes. More complicated schemes will be dictated by general knowledge of the system, and require that a family of kinetic curves be obtained rather than a single record. In the next simplest case, that of fitting two exponentials, the data and their analysis interact so that, unless the rates of the two processes are widely separated, much higher precision in

80

the data is required to permit the two rates to be determined with acceptable accuracy. Extension to two processes requires that four parameters be determined: there are now two rates and two amplitudes. It is necessary to make sure that the data points are distributed reasonably over the experimental curve so as give representation to both processes, and this may call for extending the range of data collection. Although a simple graphical method is still available - plot the data semi-log, extract the rate and amplitude of the slower process by drawing a tangent to the last part of the plot extended so as to intersect the ordinate, and then split off the faster process by plotting the difference between the tangent and the experimental curve there are relatively severe problems that are quite typical in interpreting kinetic data. It is when the rates and amplitudes have been assigned that the real limitations of the kinetic approach become evident. To make further progress, much more information is needed. If the system is well defined chemically and the number and spectra of intermediates are known, interpretation of the results and assignment of the rates is immediate. Even if the system is well defined, it is prudent to collect redundant data to allow a check of their internal consistency, repeating the experiment at different wavelengths and with different concentrations of reactants. With less well-understood systems the widest possible range of experiment is mandatory, and range should be understood to include chemical as well as physical parameters. The difference spectra for the kinetic components should be plotted, and any dependence on concentration determined and also plotted, preferably by hand, to allow time for reflection. The next step is to write down plausible schemes, taking into account what is known of the chemistry. The elements of the schemes are first- and second-order reactions, and each complete possibility may be called a model of the reaction. The distinction between curve-fitting and the use of models is not always clear, but may be drawn by considering that the one uses arbitrary mathematical elements to represent a reaction - for example, a sum of exponentials - whde the other starts with a set of chemical reactions to define the functions used. Once the possible models have been chosen, the procedure is relatively mechanical, and details have been given by many authors, often supplemented by program listings, of how to go about comparing models with experiment, e.g. Bevington [16]. The problem is one of solving a set of differential equations. It is quite exceptional to have a set of equations with an analytic solution, and numerical methods using digital computers are universal nowadays. Even where an analytic solution is available, it is quite likely to be more trouble to use than standard integration routines, often available in a packaged program. As always, rapid arithmetic is a poor substitute for common sense, and very careful thought should be given to what can be expected from optimization procedures and how best to employ them. In optimization initial guesses at the values of parameters are made, and the program seeks to improve on these using a criterion such as the sum of squared differences between each observed point and its corresponding computed value. A common and effective procedure uses the local gradient of the parameter vs. criterion surface. For two parameters, the procedure is quite analogous to walking to the highest point

81

knowing only your present height. Obviously you go upwards as steeply as the terrain allows and continue doing so until you reach a point from which all directions lead down. In the mathematical equivalent defining the gradient requires calculation, which must be repeated at each step. It is obviously important to take the longest steps possible without losing your sense of whch way is up, and good algorithms for doing this have been developed. The obvious remaining difficulty is that there may well be more than one peak on the (unknown) map. Serious numerical attempts to deal with this problem quickly run into large amounts of computation even for fairly small models. Before launching into such operations the model should be examined carefully to see if any special cases can be picked out where the reaction depends on specific parameters of the model. If they can be found, experiments under the appropriate conditions should be performed and the values of the parameters used as constants in optimization. This will greatly speed up the operation and perhaps help to make a wider search of the map grid practical. A difficulty which often arises in biochemical problems is the occurrence of widely differing rates in the same model. Broadly, the step size whch can be used in numerical integration is defined by the largest rate constant in the problem. In enzyme reactions, substrate often binds to the enzyme at something near the diffusion controlled limit. If this process is modeled and turnover is slow, enormous numbers of integration steps will be required. There are three ways of dealing with the situation. One is to assume that the enzyme is at equilibrium with its substrate throughout and calculate the populations of E and ES algebraically. If this cannot be done, it may be possible to use the full model initially, and then, after enzyme and substrate have approached a steady state, switch to a reduced model which takes this into account. Third, special procedures for dealing with these so-called 'stiff' equations have been devised. At the price of much increased calculation these permit large integration steps, but the arithmetic overhead is such that unless the step size can be greatly increased, say by two orders of magnitude, there may be no saving in time. Most experimental biochemical data suffer from considerable experimental error and it might therefore be supposed that a quite rough solution of the kinetic equations would be sufficient. If the object is to see if the model gives curves with a general resemblance to the data, this is true. For optimization, it does not apply because the local gradients are obtained by numerical differentiation. This, of course, requires that the difference between corresponding points in successive integration runs with slightly altered parameter values be subtracted from one another, and so imposes a requirement for good precision in integration. This may prevent the use of simple speed-up maneuvers, especially with stiff equations. If more than one parameter is to be assigned by optimization it cannot be expected that the values obtained will be independent of one another, and in practice the correlations between the parameters of a model are frequently high. In terms of the map simile, the peak is replaced by a ridge whch becomes sharper as the correlation rises. Such ridges offer difficulty to optimization programs, but this is of little practical importance since, if the optimum is so difficult to locate its position will be poorly defined, and only the product or quotient of the highly

82

correlated parameters can be determined. In such a case, one of the pair must be fixed by an independent experiment. An alternative way of expressing the matter is that when high correlation occurs, the information content of the data set is insufficient to define the number of parameters proposed. If optimization appears to have gone smoothly and generated a set of parameters defining a maximum, the question must follow whether the representation of the data is sufficiently good to allow the examination of models to be suspended. An important test here is to examine the run of the residuals. If the model is generating a set of curves of the right shape there will not be long runs of residuals of the same sign and, where families of curves are available, the distribution of residuals among the members of the family will not be highly correlated. In practice, this is one of the most difficult requirements to satisfy since models, of necessity simple, are being applied to complex systems. In addition, few measurements are free from systematic error which will also produce a non-random distribution of residuals. Paradoxically, the better the signal-to-noise ratio of the data, the harder it will be to satisfy the criterion of residual distribution. It is difficult to define the errors attaching to a set of parameters obtained by optimization, except in the arithmetic sense set out in the standard texts, such as Bevington. The methods used in reaching these formulas are sound, but the conditions of their use often depart widely from the assumptions made in their derivation. It is unusual to have a model and data set which allow all the parameters to be obtained directly by optimization, and many of them are therefore fixed. When the calculation of the errors in the parameters is performed the error of the fixed parameters is taken to be just what it is in the calculation, nil. The effect of having some precisely known parameters in a model on the apparent precision of the remaining ones is remarkable, and remarkably unrealistic. There may be better ways around the problem, but it can be dealt with by making an estimate of the error of each of the fixed parameters. This estimate is then used with a random number generator and a Gaussian curve to generate a set of fixed parameters. The optimization procedure is repeated and the estimates of the other parameters noted. The whole operation is repeated a sufficient number of times to allow a reasonable estimate of the errors in the parameters being varied, now free from the constraint of the fixed parameters. A second difficulty in defining the reliability of parameter values arises from the assumption in the derivation that the residuals are randomly distributed. Unless this is true, the meaning of the values obtained is uncertain. After setting out so many problems associated with parameter optimization, one non-existent difficulty may be mentioned. It is often said, presumably by persons without practical experience, that with several disposable parameters any curve may be fitted. There is an element of truth in this when only one experimental curve is available such as the oxygenation curve for hemoglobin. In this specific case it is next to impossible to obtain a data set which will define a unique set of four Adair parameters. When a family of experimental curves is available, however, the problem in practice is not that there are many solutions, but rather to find any set of parameters at all that will fit the data adequately. In addition, if the wrong model is being used, allowing another

83

parameter to vary freely seldom makes much difference to the misfit. In t h s respect reality is much more favorable than myth. This chapter has emphasized methods rather than results, simply because there have been so many kinetic investigations as to defy review, and so diverse as to defeat generalization. It is almost too obvious to mention, but generally true, that kinetic methods yield kinetic information. In short, what you know about your reaction is how fast it goes. If kinetics is all you have, then that is about all you can say about it. The more a system has been studied by other methods, the more plausible interpretation in terms of, say, chemistry, becomes possible. Such interpretation is no more or no less speculative than extrapolation from other forms of experiment. When kinetic speculation is advanced on the basis of non-kinetic experiment, then kinetic experiments have their hghest value as a criterion of its worth. As a concrete example, it was suggested some years ago, that in the deoxy (T) state, valine E l l of the beta subunits of human hemoglobin would restrict access of ligand to the heme group, and that, on ligand binding giving the R state, this hindrance would be removed. It was hypothesized that the alpha subunits, which do not have this obstruction, would bind first, the beta chains binding after the T to R transition had taken place. Kinetic experiments, however, have shown that ligand access to the beta subunits is readier than to alpha subunits when both are in the T state, and that in the beta subunits access in the T state is easier than in the R state. Furthermore, T-state beta subunits equilibrate faster with oxygen than alpha ones. In this example, if the kinetic experiments themselves are admitted to be valid, the hypothesis is shown to be wrong. This is a negative achevement - to show that a positive hypothesis is wrong - and the kinetic experiments suggest no new positive alternative. Progress in such a case is most likely if both crystallographic and kinetic experiments are accepted as correct, until evidence to the contrary appears, and one asks what other type of investigation may be used to bridge the gap between the findings. It seems reasonable to expect that the use of rapid reaction methods in biochemistry will grow considerably in the future, less through expansion in the application of conventional methods to systems in solution, than through the development and application of new methods applicable in growing areas of the subject such as cell biology. Such methods will have to be applicable to systems in which significant structure has been preserved, and be concerned with reactants as yet little studied, such as sodium, potassium, and calcium ions.

References 1 (a) Hartridge, H. and Roughton, F.J.W. (1923) Proc. R. SOC.(London) A104, 395-415. (b) Hartridge, H. and Roughton, F.J.W. (1924) Proc. Cambridge Philos. Soc. 22, 426-434. 2 Barcroft, J. (1914) The Respiratory Function of the Blood. Cambridge University Press, Cambridge,

U.K. 3 Millikan, G.A. (1936) Proc. R. Soc. (London) A155, 277-291. 4 Theorell, H. (1932) Biochem. Z. 268, 73-83.

84 5 Chance, B. (1963) In: Techniques in Organic Chemistry (S.L. Friess, E.S. Lewis and A. Weissberger, eds.) 2nd. Ed., Part 11, Vol. 8, pp. 728-748, Wiley Interscience, New York. 6 Barman, T.E. and Gutfreund, H. (1966) Biochem. J. (London) 101, 460. 7 Chance, B., Eisenhart, R., Gibson, Q.H. and Lonberg-Holm K., eds. (1964) Rapid Mixing and Sampling Techniques in Biochemistry, pp. 105, 131, 135, Academic Press, New York. 8 Roughton, F.J.W. (1963) In: Techniques in Organic Chemistry (S.L. Friess, E.S. Lewis and A. Weissberger, eds.) 2nd. Ed., Part 11, Vol. 8, Ch. 14, pp. 704-727, Wiley Interscience, New York. 9 Gibson, Q.H. and Roughton, F.J.W. (1955) Proc. R. Soc. (London) B143, 310-334. 10 Gibson, Q.H. and Milnes, L.H. (1964) Biochem. J. (London) 91, 161-171. 11 Gibson, Q.H. (1969) In: Methods in Enzymology (K. Kustin, ed.) Vol. 16, pp. 187-228, Academic Press, New York. 12 Eigen, M. and De Mayer, L. (1963) In: Techniques in Organic Chemistry (S.L. Friess, E.S. Lewis and A. Weissberger, eds.) 2nd. Ed., Part 11, Vol. 8, pp. 892-1054, Wiley Interscience, New York. 13 Henry, E.R., Sommer, J.H., Hofrichter, J. and Eaton, W.A. (1982) J. Mol. Biol. 166, 443-451. 14 Ilgenfritz, F. and Schuster, T.M. (1974) J. Biol. Chem. 249, 2959-2973. 15 Asher, S.A. (1981) In: Advances in Enzymology (E. Antonini, L. Rossi-Bernardi and E. Chiancone, eds.) Vol. 76, pp. 371-416, Academic Press, New York. 16 Bevington, P.R. (1969) Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New York.

A. Neuberger and L.L.M. Van Deenen (Eds.) Modern Physical MethoriS in Biochemistry, Part B 1988 Elsevier Science Publishers B.V. (Biomedical Division)

85

Q

CHAPTER 4

High performance liquid chromatography of nucleic acids METIN COLPAN a

a

and DETLEV RIESNER

DIAGEN GmbH, Niederheiderstr. 3, 0-4000 Diisseldorf 13, FRG and Institut f i r PhysikaIische Biologie, Universitat Diisseldorf; Universitatsstr. I , 0-4000 Diisseldorf I , FRG

1. Introduction Isolation of altogether different but well-defined nucleic acids is of major interest in present-day biochemistry, biophysics, molecular biology and gene technology. For example, in biophysical chemistry of nucleic acids large amounts of homogeneous nucleic acid material are needed. The requirements range from synthetic oligonucleotides with defined sequences which are used to determine the elementary parameters of nucleic acid structure and stability, up to large natural nucleic acids such as plasmids [l]which are the subject of studies about supercoiled structures and nucleic acid topology. For biochemical studies on RNA, e.g. tRNA, viroid RNA [2] or viral RNA [3], highly purified fractions of these RNAs from natural sources have to be prepared. Often, one is confronted with the difficulty of those RNAs being present in the cell together with a vast excess of other, sometimes quite similar, nucleic acids. Other new applications of HPLC have emerged from recent developments in molecular biology and gene technology. Routinely, for the different steps of the cloning and sequencing procedures synthetic oligonucleotides, DNA fragments and plasmids must be prepared in great purity. Purity alone, however, does not suffice as a specification; in addition, they are supposed to be highly active in a variety of enzymatic reactions and biological transformations [4]. Another new field of HPLC of nucleic acids arises in diagnostic applications for medicine and phytopathology. In these new areas of application too, hghly purified probes of recombinant DNA or RNA will be required, e.g. for testing for infectious diseases or for genetically determined disorders. Interactions of nucleic acids with the chromatographic resin, are very much dependent on the structure of the nucleic acids. Nucleic acids, natural as well as synthetic ones, may belong to very different structural types. In this respect, a major Abbreuiations: bp

= base pairs; GPC = gel permeation chromatography; HIC = hydrophobic interaction chromatography; IEC = ion-exchange chromatography; RPC = reversed phase chromatography; SEC = size exclusion chromatography.

86

difference exists between single-stranded and double-stranded nucleic acids, resulting in characteristic differences in flexibility, shape, charge density and hydrophobicity [6,7]. Another classification of nucleic acids differentiates between DNA and RNA, whether present in single-stranded or double-stranded form. In themselves, double-stranded forms of DNA on the one hand and of RNA on the other also exhibit differences in charge density, hydrophobicity and hydrodynamic flexibility. Furthermore, very special forms of double-stranded DNA do occur, e.g. when double-strands form covalently closed circles as they do in supercoils. In contrast most single-stranded RNAs of natural origin may be considered as having a globular structure with a high degree of internal organization. In summary, nucleic acids do not only extend over a molecular weight range of several orders of magnitude, they may also belong to different or even opposite structural types. Corresponding to the molecular variations in size, structure and charge, various chromatographic principles have been applied to the separation of nucleic acids. It is primarily the technologies of size exclusion-, anion-exchange-, hydrophobic-, and RPC-5-chromatography that have been applied with excellent or at least partial success to the fractionation of nucleic acids. This chapter will focus on the discussion of these technologies. For a treatise of general theory and basic applications of HPLC, the reader may refer to textbooks ( e g [8,9]).

2. Techniques 2.1. Size exclusion chromatography Size exclusion (SEC) or gel permeation chromatography (GPC) is the most widely used chromatographic method in biochemistry. The biomolecules are separated by size during elution through a neutral and hydrophilic packed bed of porous particles. Large molecules are excluded from the pores and elute first, whereas small molecules totally invade the pores and elute last. Ideal SEC would imply that no interaction occurs between macromolecules and chromatographx resin. In practice, however, many interactions such as adsorption, hydrophobic or ionic interactions, affect the chromatographic separation. Therefore, it is important to identify and minimize these residual interactions. Nucleic acids are separated in SEC by partitioning them between mobile phase and stationary phase within the pores of a support. Those with a hydrodynamic diameter larger than the pore diameter are excluded and eluted with the void volume V, which represents the interstitial volume between the particles of the resin. Smaller nucleic acids partially penetrate the support pores and have an elution volume V , described by the with V, being the pore volume and K D being the equation V ,= V, + K D . distribution coefficient with values between 0 for exclusion and 1 for total penetration. Since the penetration is shape dependent, generally applicable calibration curves of the molecular weight vs. the retention volume do not exist. Calibration curves determined with polyethyleneglycol, dextran or proteins cannot be transferred to nucleic acids. Fortunately, during the last years, the properties of the most

87

common SEC columns have been evaluated for nucleic acids. These data facilitate the choice of the appropriate column for a specific separation problem. An example of the separation of different cellular RNAs is given in Fig. 1. The columns used in high performance SEC are based on resins of completely organic nature or, on silica thinly coated with a hydrophilic surface. Currently, several organic resins for high performance SEC are commercially available. They are listed in Table 1. Although these resins may exhibit slight hydrophobic interactions with proteins, particularly at high ionic strength, such interactions are not detectable with nucleic acids. This is because nucleic acids are highly hydrophilic polyanions and, therefore, are prevented from hydrophobic contacts by their strong hydration shell. The hydrophilicity is more strongly expressed with double-stranded than with single-stranded nucleic acids. All inorganic supports presently available are based on porous silica gel. Non-reversible adsorption of nucleic acids on the silica surface has been overcome by

TABLE 1 High-performance SEC columns for nucleic acid separation Name

Support material

Organicpolymers Spheron P300

PlOOO Superose 6B 12B TSK G 3000PW G 4000PW G 5000PW G 6000PW

Hydroxyethylmethacrylate Hydroxyethylmethacrylate Cross-linked agarose Cross-linked agarose Hydrophilic polyether Hydrophilic polyether Hydrophilic polyether Hydrophilic polyether

Pore diameter (A) 300

300000

Reference

a, [711

lo00 b

200

C

500

1000

Silica-based supports Zorbax GF150 Diol GF250 Diol GF450 Diol

150 250 450

TSK G 2000SW 3000SW 4000sw

125 250 400

Hydrophilic polymer

Exclusion limit (daltons)

lo00000

d

50000 100o00 300000

C

(a) Lachema, Bmo, CSSR; (b) Pharmacia, Uppsala, Sweden; (c) Toyo Soda, Kyoto, Japan; (d) Du Pont, Wilmington, DE, USA.

88

Elution time ( h )

Fig. 1. SEC of cellular RNA. Column: TSK G 4000 SW (7.5 X 600 nm); sample: ribosomal 16 and 23 S RNA ( E . coli), 10 pg each, and 9 p g tRNA (wheat germ); chromatographic conditions: 0.1 M Na-phosphate, 0.1 M NaC1, p H 6.8; 100 pl/min; 22" C. From 1141.

coating the silica surface with hydrophilic groups. The surface coating of these supports is either of the brush-type carrying diol-groups, or of the type of a hydrophilic polymeric phase. More details are listed in Table 1. In addition to the materials listed in Table 1, the following are available: LiChrospher-diol (E.Merck), Nucleosil-Diol (Macherey-Nagel), and SynChropak GPC (Synchrom). The latter, however, have not yet been applied to nucleic acid fractionation, although they do belong to the diol-type coated supports. 2.2. Anion-exchange chromatography Anion-exchange chromatography (IEC) is a very obvious method for the fractionation of polyanions such as nucleic acids. This principle has been applied as long as nucleic acids have been purified by chromatography. The development of high-performance IEC has led to an increase in resolution and an extension of this methodology to high molecular weight nucleic acids. In any anion exchange technique, the negatively charged nucleic acids are adsorbed on positively charged groups of the resin. They are displaced from the resin, by the ions of an increasing salt gradient, in an order of sequence corresponding to the number of their interacting charges. As a rule, IEC is able to separate nucleic acids with a higher resolution than SEC. As with SEC, two types of support materials are being used for IEC. Completely organic resins as well as surface-modified silica-gel resins are available; they are listed in Table 2. TSK-DEAE 5PW [ll]and Mono-Q [12] are organic polymers with surface charges. TSK-DEAE 3SW [ l l ] is a polymer coated silica-gel, whereas

89 TABLE 2 High-performance IEC columns for nucleic acid separation Support material

Functional group

Pore size (A)

Reference

Hydroxylated polyether

Diethylamino

loo0

C

Hydrophilic acrylic polymer

Quarternary diethylamino

Silica-based supports TSK-DEAE3-SW

Coated silica

Diethylamino

250

C

Nucleogen DEAE 60 DEAE 500 DEAE 4OOO

Coated silica Coated silica Coated silica

Diethylamino

60 500

e, f

Polyethylene imine coated silica

Prim. and sec. amino

SynChropak AX 300 AX 500 AX lo00

Coated silica Coated silica Coated silica

Amine Amine Amine

Partisil SAX

Coated silica

Quarternary diethylamino

Name Organic poIymers TSK-DEAE 5PW

Mono-Q

PEI-Silica

b

4000

100

[10,68,69]

300 500 lo00

g

100

h

(a)-(c), see Table 1; (e) Diagen, Dusseldorf, F.R.G; (f) Macherey-Nagel, Duren, FRG; (9) SynChrom, Linden, IN, USA; (h) Whatman, Maidstone, Kent, UK.

Nucleogen DEAE 1131 is a brush-type coated silica gel. A priori, one would not expect the resins listed in Table 2 to be affected by non-ionic interactions. Available chromatographic data (see below), however, indicate slight hydrophobic interactions. All anion-exchange resins are based on porous supports. The pores have to meet two requirements, (a) they have to enlarge the interacting surface, and (b) they have to allow for a free penetration of the nucleic acids in orderoto avoid size exclusion effects. Consequently, resins with small pores (typically 100 A) may be used only for oligonucleotides, resins with intermediate pores (500 A) primarily for medium-sized nucleic acids (in particular for globular RNA up to 150000 daltons), and large-pore resins (4000 A) preferably for high molecular weight nucleic acids, for example plasmid DNA of up to 15 X lo6 daltons. Fig. 2 shows the fractionation of oligo (rA) with chain lengths of 3 to 37 nucleotides on TSK-DEAE 5PW. Similar results have been reported for Nucleogen DEAE 60 [16] and MONO-Q 1171. As an example for IEC separation of medium-sized nucleic acids, the elution profile of a crude plant RNA extract on Nucleogen DEAE 500 is shown in Fig. 3. A comparable resolution was obtained on TSK-DEAE 5PW although a slower elution was necessary [18]. The resin with the

90

E l u t i o n t i m e (min)

Fig. 2. IEC of synthetic ribo-oligonucleotides. Column: TSK DEAE-5 PW (7.5 x75 mm); sample: 150 pg of homoribo-oligonucleotides (rA)"; chromatographicconditions: linear gradient from 0 to 1 M KC1 in 200 min; 25 mM K-phosphate, pH 5.5; 1 ml/min; 14 bar; 22OC. From [15].

largest pore size available Nucleogen DEAE 4000 (4000 A pore size) needs to be used for isolation of supercoi1ed.plasmidsof MW 4 X lo6 (cf. Fig. 4; [16]). Smaller pores have the advantage of a higher surface area and, thus, higher nucleic acid binding capacity. Larger pores, on the other hand, always show increased resolution with only one exception having been reported for oligo (rA) of a chain length up to 13 [16]. The user may be well advised to apply the largest pore sizes available in order to achieve highest resolution and medium-sized pores only if very high preparative capacity is needed. A wide variety of mobile phases has been used for the elution of nucleic acids from IEC-columns. No consistent interpretation of the influence of the buffer/salt combination on the resolution has been given so far, but some of the empirical results are of practical importance. The most widely used Tris/NaCl combination is not always likely to be the best choice. As investigated with Nucleogen columns in greater detail, phosphate buffer most of the time shows superior resolution with NaCl or KC1 being the eluting salts [20]. Additives such as 4-6 M urea or 25-50% formamide have been shown to achieve further increases in resolution and contribute significantly to avoid cross-contamination (Fig. 5). Under normal chromatographic conditions, these additives do not denature the double helical structure of nucleic acids, but eliminate residual interactions between different nucleic acid molecules as well as between nucleic acid and chromatographic resin. Hydrophobic interactions and hydrogen bonds are considered most likely contributors to these unspecific interactions. Also, the gradient slope has some influence on the resolution. Therefore, one has to look for the best compromise between highest resolution, i.e. a shallow gradient,

91

Fig. 3. Preparative and analytical IEC of crude RNA extract. (A) Preparative IEC. Column: Nucleogen DEAE-500 (12 x 150 mm); sample: 30 mg crude RNA extract from viroid-infected plants; chromatographic conditions: linear gradient from 250 mM to 1 M KCl in 400 min; 20 mM K-phosphate, pH 6.6, 0.1 mM EDTA, 5 M urea; 2 ml/min; 21 bar, 22" C. (B) 5% polyacrylamide gel electrophoresis of the peak fractions from (A) as indicated in the chromatogram; the unfractionated sample is in slot M. (C) Analytical IEC. Column: Nucleogen DEAE-4000 (3 X 50 mm); sample: 20 pg of the sample from (A); chromatographic conditions: linear gradient from 250 mM to 1 M KCl in 45 min; 20 mM K-phosphate, pH 6.6, 0.1 mM EDTA, 5 M urea; 1 ml/min; 42 bar; 24OC. From [16].

and shortest separation time, i.e. a steep gradient. Salt gradients with an increase between 2 and 20 mM/min have been found to give the best results [20]. In contrast to SEC, the influence of the flow rate is fairly minor in the case of IEC. In most applications, no increase in resolution has been achieved by elevated temperatures. Exceptions have been reported only for partially self-complementary oligonucleotides where intermolecular interactions could be avoided by raising the temperature to 60 C and adding 50% formamide [21]. 2.3. Reversed phase and hydrophobic interaction chromatography

Reversed phase (RPC) and hydrophobic interaction chromatography (HIC) are based on very similar types of interactions; they have been regarded as different

92

Fig. 4. IEC of plasmids. Column: Nucleogen DEAE-4000 (6 X 125 mm); sample: 5 p g plasmid pBR322 from a cleared lysate without RNaseA digestion: chromatographic conditions: linear gradient from 250 to 1250 mM KC1 in 50 min; 30 mM K-phosphate, pH 6.5, 5.5 M urea; 1 ml/min; 36 bar; 22” C. The gel electrophoretic analysis shows the cleared lysate (CL) and the plasmid (S) in the supercoiled form. From ~91. b

a

I

A26( 0.01

C 1

0

20

40

I

30

6o t [mid

Fig. 5. Influence of urea on the resolution of DNA fragments. Column: Nucleogen DEAE-4000 (6 x 125 mm); sample: 5 p g of restriction fragments from the plasmid pSP 64 after cleavage with the restriction enzyme HaeIII; the lengths of he fragments were: 65 bp (a’), 69 bp (b’), 78 bp (c’), 126 bp (d’), 182 bp (e’), 269 bp (f ’), 426 bp (g’), 490 bp (h’), 537 bp (i’), 616 bp (k’); chromatographic conditions: (a) linear gradient from 700 to 1200 mM NaCl in 100 min; 30 mM Na-phosphate, pH 6.0, 6 M urea; 1 ml/min; 65 bar: 23OC; (b) linear gradient from 700 to 1200 mM NaCl in 100 min; 30 mM Na-phosphate, pH 6.0, without urea; 1 ml/min; 45 bar; 23O C. From [20].

93

I

50

100

150

Time ( m i n )

Fig. 6. RPC of homoribopolynucleotides. Column: Varian MH,, (CIS)(4 X 30 mm); sample: 10 pg of a mixture of homoribopolynucleotidespoly(U), poly (I), and poly(A); chromatographic conditions: linear gradient from 100 mM NH,-acetate, pH 6.4 to 40%acetonitrile:water (1:1) in 200 min; 0.2 ml/min; ambient temperature. From [25].

concepts more for historical than for physicochemical reasons. RPC of nucleic acids has its origin in the technique of countercurrent distribution of tRNA [22], whereas HIC was adapted from protein fractionation (for review see [23]). Both techniques employ a resin with hydrophobic surface to which the nucleic acid is adsorbed by hydrophobic interaction. They are differentiated, however, by characteristic hydrophobic parts of the nucleic acids involved in the interaction. In RPC, hydrophobicity is established by ion-pair formation between negative phosphates and an alkyl-ammonium salt. Due to this reason RPC of nucleic acids is often called ion-pair chromatography which indeed should be its name of choice. The adsorbed nucleic acids are eluted by an increasing gradient of organic solvents, typically acetonitrile or isopropanol. Furthermore, the hydrophobicity of the heterocyclic bases of the nucleic acids contributes to their overall hydrophobicity. These contributions, however, might be significant only in the case of single-stranded nucleic acids. An example for the separation of different homoribopolymers is given in Fig. 6. In the case of double-stranded nucleic acids, hydrophobic interactions are compensated by the intramolecular structure. Therefore, as a general rule doublestranded nucleic acids elute earlier than single-stranded ones. In HIC, nucleic acids are adsorbed to the hydrophobic surface by salting out from the aqueous mobile phase. The adsorbed nucleic acids are eluted by a decreasing salt gradient which re-dissolves the nucleic acids in the aqueous mobile phase. This type of chromatography is similar to the method of fractionated

94

TABLE 3 High performance HIC and RPC columns for nucleic acid separation Functional group Phenyl

Name TSK Phenyl5 PW

Support material Hydroxylated polyether

Vydac RP Pro RPC PEP-RPl TSK 304 308 SynChropak LiChrosphere RP18 Biosil ODS Bondapack

Coated silica Coated silica Coated silica Coated silica Coated silica Coated silica Coated silica Coated silica Coated silica

Nucleosil 100-Cl8 120-C18 300-C18

Coated silica Coated silica Coated silica

Cl,

Varian MH,,

Coated silica

CIS

Pore size (A) lo00 330 300 300 330 330 300 100

100 100

‘18

Cl,

100 120 300

Reference C

g

k d m f

j

(b)-(g) see Tables 1 and 2; (i) Vydac, Hesperia, CA, USA; 6) Varian, Walnut Creek, CA, USA; (k) E. Merck, Darmstadt, FRG; (1) BioRad, Richmond, CA, USA; (m) Waters, Milford, MA, USA.

precipitation. Similarly, as with the precipitation of nucleic acids with high salt, the adsorption is stronger for single-stranded nucleic acids whereas it hardly comes into play for double-strands. In both cases, however, it increases with chain length. The hydrophobic surfaces for RPC are alkyl-groups, typically c8-and C,,-phases, whereas for HIC, phenyl- and t-butylphases are most common. As in SEC and IEC the chromatographic supports for the hydrophobic surfaces are organic polymers or porous silica. Table 3 lists the resins for hydrophobic chromatography of nucleic acids. Investigations regarding a systematic variation of chromatographic parameters such as temperature, gradient slope, flow rate, buffer conditions have been undertaken only in a few cases (e.g. [24,25]). Only minor influences have been found. 2.4. RPC-5and other mixed mode chromatography RPC-5 and other mixed mode chromatographic techniques are based on ionic as well as on hydrophobic interactions. RPC-5 is the earliest of these techniques having been introduced more than 20 years ago [26].The resin applied originally consists of a charged reversed-phase matrix with a quaternary ammonium derivative (such as methyltrialkyl (C8-Cl,,) ammonium chloride) being adsorbed on a non-porous polymer support such as Plaskon or Teflon. In contrast to other HPLC-resins, the surface-forming groups of RPC-5 are physically adsorbed to the polymeric support and are not covalently bound; therefore RPC-5, in principle, can be called a

95

-

1600

E 3

1400

1200

N U al

1000

: ?

2

064 800

L

2

fl

600

Q

400

200

0

0 200

250

300

350

Retention volume (ml)

Fig. 7. Ionic-hydrophobic interaction chromatography of tRNA. Column: trioctylmethylammonium chloride-treated ODS-Hypersil (4.6 X 250 mm); sample: 2 mg of bulk tRNA from baker's yeast, showing amino acceptor activity above background for valine (Val), isoleucine (Ile), arginine (Arg), lysine (Lys), serine (Ser), phenylalanine (Phe) and tyrosine (Tyr); chromatographic conditions: 100% buffer A (0.5 M ammonium acetate, pH 5.0) to 60% A, 40% buffer B ( 5 M ammonium acetate, pH 5.5) in 1080 min; 0.5 ml/min; 35 O C. The continuous line represents the absorbance at 260 nm; the broken lines the amino acid acceptor activities. From [28].

liquid-liquid chromatography procedure. More recently, resins with a covalently bound mixed-mode surface have been developed by McLaughlin and coworkers [27,28]. They have used partially modified amino-propylsilica with different alkyl chains and aryl groups. In contrast to RPC-5, the resins of McLaughlin and his coworkers allow the use of organic solvents as modifiers. Because ionic interactions prevail in mixed-mode resins, elution of the adsorbed nucleic acid is achieved by a salt gradient. As reported in the literature, elution times in mixed-mode chromatography are approximately five times longer as compared with IEC, RPC and HIC. Chromatographic parameters have been optimized systematically by Wells and coworkers [29-311 and by McLaughhn and coworkers [27,28,32]. Under optimum conditions, they obtained very good results of resolution with oligonucleotides, tRNA [27,28,32]and DNA fragments [29-311. An example of tRNA fractionation is given in Fig. 7. Up to now, however, long separation times, compressibility with pressure, and poor or non-existing commercial availability have impeded the successful application of mixed-mode chromatography in a larger number of research laboratories. 2.5. Sample preparation and recovery Most commonly, nucleic acid samples are submitted repeatedly to phenol extraction, precipitated with ethanol and dissolved in low salt buffer. Prior to chromatog-

96

raphy, the samples are adjusted to starting conditions by adding concentrated buffer solutions. Whereas sample preparation is a standard procedure, the most convenient procedures for sample recovery may be less well known to the reader. In SEC and RPC, nucleic acid fractions may be precipitated with ethanol after elution, with no added steps. In contrast, ethanol precipitation cannot be carried out with IEC and HIC because high salt concentrations would have to be used for elution and therefore, co-precipitation of the vast excess of salt would occur. The high salt content could potentially be removed by dialysis, but such a procedure would be time consuming and possibly degradation of the nucleic acids could lead to the loss of sample. The following procedures may be recommended as rapid and reliable ways for recovering and concentrating nucleic acids from eluted fractions. The nucleic acids are to be precipitated by either polyethyleneglycol [20] or isopropanol [33]: Polyethyleneglycol: solid polyethyleneglycol 6000 is added and dissolved up to a final concentration of 10%(w/v), the DNA is allowed to precipitate on ice for 2 h or longer. Zsopropanol: samples containing KC1 or NaCl and 4-6 M urea or 25-60% formamide are diluted with 25%water. The nucleic acids are then precipitated with 1 vol. isopropanol for 1 h at - 20 O C. After centrifugation, the pellet is washed with 75% ethanol/water. Thereafter, it can be used without further purification. Using this procedure, even quantities of 10 ng/ml DNA can be precipitated with recovery of 90%.

3. Applications 3.1. Oligonucleotides Oligonucleotides of defined sequences have been synthesized and purified for physicochemical studies, for sequencing and, with increasing importance in molecular biology, as synthetic segments of genes. Modern developments in oligonucleotide research were reviewed by Gassen and Lang [34]. In the beginning, fractionations of oligonucleotides up to chain lengths of about 20 nucleotides were camed out on cellulose or dextran based anion exchangers [35]. The subsequent introduction of HPLC to oligonucleotide separation, initially contributed more to a shortening of separation times rather than to increasing resolution. Silica gels with bonded anionic groups were applied [36-381. At about the same time reversed-phase resins (silica gels with C,, alkyl chains) were introduced 1391. Following these new trends, several authors reported successful separations of oligonucleotides with IEC [17,40-481 and RPC [45,49,50]. Later, oligonucleotides have been satisfactorily separated by mixed mode chromatography, either on RPC-5 [51] or on silica gel with a covalently bound mixed mode surface [27,32]. The need for long synthetic oligonucleotides with chain lengths up to 100 nucleotides triggered an improvement of the chromatographic resins. Obviously,

91

-06 2

002N Y)

4

001 -

07’ 0

20

40

60

80

100

Tlme (min)

Fig. 8. IEC of 40- to 60-base oligodeoxyadenylates. Column: quatemked polyethylenimine-coated silica (4.1 X 50 mm); sample: 30 p g of 40- to 60-base oligodeoxyadenylate; chromatographic conditions: linear gradient from 80% buffer A (0.05 M K-phosphate, 15% (v/v) acetonitrile, pH 5.9) 20% buffer B (1.0 M ammonium sulfate, 0.05 M K-phosphate, 15% (v/v) acetonitrile, pH 5.9) to 50% A, 50% B in 120 min; 0.5 ml/min; ambient temperature. From [lo].

however, in recent years only ion exchangers and mixed-mode resins could be substantially improved. These improved resins are listed in Table 2 and have been dealt with in sections 2.2 and 2.4. An example of a fractionation of ribo-oligo A up

1

0

I 20

I 40

Time (rnin)

Fig. 9. IEC of a synthetic-29 meric oligodeoxynucleotide.Column: Nucleogen DEAE-4000 (6 X 125 mm); sample: 10 pg 29-meric oligodeoxynucleotide; chromatographc conditions: linear gradient from 150 to 500 mM KCl in 70 min; 20 mM K-phosphate, 5 M urea, pH 5.5; 1 ml/min; 32 bar; ambient temperature. From [191.

98

to a chain length close to 40 on a commercial ion-exchanger is shown in Fig. 2. A further improvement of resolution, as shown in Fig. 8, has been reported recently by Regnier and coworkers [10,68,69]who synthesized a surface of quaternized cross-linked polyethylenimine. A typical example of an oligonucleotide separation after synthesis in an automatic syntheziser is given in Fig. 9. A 29-mer containing eight sequences due to a mixed synthesis in two positions was purified on Nucleogen DEAE 4000. In order to recover in a single narrow peak all sequences desired, it is important that the ion exchanger is fractionated according to chain length with no sizeable influence of the base composition. High resolution of a series of homooligonucleotides was reported by Bischoff and McLaughlin [321 employing their own ionic-hydrophobic resin. With this mixed-mode resin, a marked influence of the base composition on the separation of synthetic oligonucleotides was to be anticipated in analogy with the experimental findings with tRNA [32]. 3.2. Natural RNA

tRNA has been the first natural RNA attracting wide interest because of its purification by means of HPLC. Kelmers et al. [26] developed their RPC-5 resins originally for the chromatography of tRNA. RPC-5 and anionic-hydrophobic chromatography appear to be, a priori, the appropriate methods for the isolation of specific tRNAs because firstly, these techniques do include hydrophobic interactions and, secondly, specific tRNAs differ in their hydrophobicity due to their content of modified bases. On the other hand, SEC and pure IEC are not supposed to be able to fractionate tRNAs which are very similar in size and charge. The fractionation of tRNA on polyethylenimine-coated silica [101 is most probably due to residual hydrophobicity of the resin and due to residual conformational effects of different tRNAs. An updated review of RPC-5 of tRNA is given by Singhal [52]. The best resolution of specific tRNAs and their isoacceptors, respectively, has been achieved on a silica-based ionic-hydrophobic resin (see section 2.4) [28,32]; an elution profile is given in Fig. 7. Similar results were reported by Rassi and Horvath [531. The most abundant cellular RNAs such as tRNA, and ribosomal RNAs such as 5S, 16s and 23s RNA assume well-defined globular structures. This may be the reason why good separation of these components is achieved by SEC on Superose 6 [54] and TSK-Gel 4000 SW [55,56]. Separation of 16s from 23s RNA has been achieved also by HIC on TSK phenyl-5PW [57] and by IEC on TSK DEAE 5PW [Ill. Messenger RNAs cover a range of a few hundreds to several thousands of nucleotides; they cannot be characterized by a uniform globular structure. For fractionation of mRNA, SEC with TSK-G 4000 SW [56,58] and RPC [24,59,60] were employed, without, however, achieving high resolution. Although the application of IEC to mRNA has not been reported as yet, fractionation ought to work with success comparable to the other methods. Viral and viroid RNAs have been isolated from crude RNA extracts of host plants by IEC on Nucleogen DEAE 500 [13,16], on TSK DEAE 5PW [18] and, by

99

a

0

50

100

Time (rnin)

Fig. 10. IEC of a mixture of viral and cellular RNA. Column: Nucleogen dimethylamino-1000 (12.7 x 50 mm); sample: mixture of tRNA (a), 5SRNA (b), 7SRNA (c), RNAS from cucumber mosaic virus in the single-stranded form (d) and in the double-stranded form (9, viroid RNA (e), and RNA from phage MS2 (g); chromatographic conditions: linear gradient from 250 to 1500 mM KCl in 150 min; 20 mM K-phosphate, 0.1 mM EDTA, 5 M urea, pH 6.6; 2 ml/min; 19 bar; 22O C. From 1161.

SEC on TSK G 4000 SW [61]. IEC seems to be advantageous over SEC in respect to resolution, capacity and speed. An example of IEC was given in Fig. 3. In Fig. 10, the resolution of a mixture of viral and viroid RNA is being shown. Finally, in the case of cucumber mosaic virus associated RNA, a single-stranded form has been successfully separated from a double-stranded form [161.

3.3. DNA fragments As soon as DNA fragments of well-defined length and sequence had been obtained by restriction enzyme digestion (for review see [l]), their preparative isolation provided an obvious challenge for HPLC. The first highly resolved DNA-fragment preparations were reported by Wells and coworkers on RPC-5 resins [29-311. An example is shown in Fig. 11. More recently SEC with TSK G 4000 SW [55,62,64,65,70] and with Superose 6 [54], and IEC with TSK DEAE 5PW [11,63], with Nucleogen DEAE-4000 [20] and with Mono-Q [67] were introduced for DNA fragment preparation. In Figs. 12 and 13 elution profiles of DNA fragments of comparable size are shown, either being chromatographed with SEC or IEC. At present the highest resolution appears to be achievable with IEC. DNA fragments up to 5000 bp can be processed with IEC and are base line separated from a fragment of 2300 bp as demonstrated by Fig. 13. The capability of separating fragments of this large size fully meets the requirements for HPLC in molecular biology as the size of even large genes is included in this range. However,,resolution as high as e.g. in Fig. 13, cannot be achieved with quantitation of DNA in the

100

Fract ;on number

I

I C 60

I 06 5

I 070

M o l a r i t y of KCI

Fig. 11. RPC-5 of DNA fragments. Column: RPC 5 (1.5 X 150 mm); sample: 50 p g of DNA fragments from the plasmid pRZ2 digested with the restriction endonuclease HueIII; the fragment sizes (in bp) are: A, 850; B, 575; C, 465; D,425 (three fragments); E, 255; F, 203; G, 180; H, 169; I, 135; J, 117; K, 102; L, 98; M, 85; N, 69; 0,.43; chromatographic conditions: linear gradient from 0.55 to 0.75 M KCl in 180 min; 10 mM Tris-HC1, pH 6.8, 2 mM Na-thiosulfate, 0.1 mM EDTA; 0.2 ml/min; 43°C. From [29].

P E cr

Y

u-

M

Y

Y

311 bp 249 bp 200 bp 151 bp 140bp

Y

8 #

553 bp 427 bp

Y

.* Y

100 bp 66 bp

48 bp 2

3

3

4

5

Time (h)

Fig. 12. SEC of DNA fragments. Column: (a) TSK-G 4000 SW (7.5 X 600 nm); (b) tandem TSK-G 4000 SW (7.5 X 600 mm); and TSK-G 3000 SW (7.5 X 600 mm); sample: (a) 5 pg of DNA fragments from the phage $X 174 after digestion of the RF DNA with the restriction endonuclease H i n f l ; the sizes of the fragments (in bp) are indicated in the figure; (b) 10 pg of sample (a); chromatographic conditions: 50 mM triethylammonium acetate, pH 7.0; 6 ml/h; ambient temperature; (c) electrophoretic sepiration of lyophilized chromatographic fractions on 10%polyacrylamide gel. From [64].

101

I 0

I

20

I

40

Time (min)

Fig. 13. IEC of DNA fragments. Column: Nucleogen DEAE-4000 (6x125 mm); sample: 10 pg of a mixture of DNA fragments with 19, 30, 34, 41, 45, 74, 168, 296, 4 X 344, 881, 2946, 5095 bp in the order of their elution; the small peak at 37 min is from switching the sensitivity of the optical recorder; chromatographic conditions: linear gradient from 250 to 750 mM KC1 in 15 min and 750 to 1500 mM KCI in 50 min; 30 mM K-phosphate, 5 M urea, pH 6.6; 1 ml/min; 32 bar; ambient temperature. From [191.

milligram range. Daily laboratory routine, however, calls for rapid isolation of smaller quantities (e.g. 1-5 pg) for cloning work. Should larger amounts of a particular fragment be required, they may be obtained by isolating the fragment in small amounts, subcloning it in a new vector system which then, in HPLC, will yield only two peaks: the cut-out fragment and the rest of the plasmid. The separation of 2 mg of a 359 bp fragment from 7 mg residual plasmid in a single run has been reported by Hecker et al. [20]. 3.4. Plasmids

In most laboratories, plasmids are used as cloning vehicles for recombinant DNA studies. Many attempts have been made for rapid isolation of supercoiled plasmid DNA. The conventional method used to be preparation of plasmids by banding them in a CsCl density gradient [4]. This procedure, however, needs prolonged ultracentifugation at high speed and large amounts of CsC1. Chromatographic preparation of plasmids has been described by Wells and coworkers with RPC-5 resin [31]. However, Wells’ procedure has not been followed by other authors. With the simplicity of a routine procedure, the isolation of supercoiled plasmids, was carried out on Nucleogen DEAE-4000 columns [16]. Typically, 25 pg of plasmid could be purified within 30 min starting with a crude cell lysate. This method has

102

0.0.

0

L

aJ 0

d

5

0

15

30

Time (min)

Fig. 14. IEC of supercoiled, relaxed, and linear plasmid DNA. Column: Nucleogen DEAE-4000 (6 X 125 mm); sample: 4 pg of supercoiled plasmid pBR 322, 1.5 pg of the plasmid pBR 322 linearized with the restriction endonuclease BamHI; the relaxed form is generated from the supercoiled form during storage; chromatographic conditions: linear gradient from 750 to 1500 mM KCl in 120 min; 20 mM K-phosphate, 5 M urea, pH 6.6; 1.5 ml/min; 45 bar; ambient temperature. From [19].

been scaled up for the preparations of milligram amounts [19]. The plasmid peak in Fig. 4 contains only supercoiled plasmid as is apparent from the gel electrophoretic analysis in the inset of Fig. 4. Supercoiled plasmids could even be resolved from their relaxed and linear forms with a reduced gradient slope ([16,66]; cf. Fig. 14). Furthermore, high activities of the isolated plasmid in enzymatic reactions in addition to enhanced activities in biological transformations have been reported for separations with this resin [19,66].

4. Concluding remarks In this chapter we have attempted to demonstrate that the present state of HPLC is such that many preparative and analytical problems in nucleic acid research may be solved. From the examples described, it should be obvious that the advantages of HPLC over other techniques lie in some cases in the capacity, in others in the resolution or yield, and in all cases in the greater speed with which separations may be made. When experimentally tested, the results have shown that the ‘biological quality’ of the samples prepared by HPLC is very high; biological quality summarizes enzymatic activity and - more importantly - biological transformation activity.

103

Future development may go in directions we cannot predict at this stage. A few points, however, may be made. Basic qualities of the HPLC matrices, such as their mechanical and chemical stability, will be continually improved upon but no major alterations are needed or expected in this field. More progress may be expected from those refinements in the chromatographic matrices which will allow application to problems hitherto inaccessible by HPLC. For example, at present no DNAs larger than 20 kilobases have been dealt with. Hence, one would welcome the ability to fractionate whole phage DNA or large genomic DNA, probably in the range of up to 200 kilobases. Not only has chromatographic resolution not yet been achieved in this range, but there also exists the principal problem of the breaking of the DNA due to hydrodynamic shearing. Another area of interest is the fractionation of mRNA with higher resolution than has been achieved so far. This would facilitate the screening procedures in gene cloning. Finally, larger oligonucleotides with a chain-length difference of one nucleotide should be separable with HPLC. The improvement in HPLC of oligonucleotides should keep up with the development of automatic gene synthesizers which are able, at present, to produce oligonucleotides of one hundred or more units. Instrumentational improvements are necessary for the use of microtechniques. For example, during gene cloning work only amounts of 1 to 50 ng of nucleic acids are sometimes available for preparation. This type of work requires special equipment which may be used for preparative as well as for analytical purposes on a microscale. Although improvements of various kinds are under consideration as outlined above, we may conclude that the existing HPLC technology is more advanced than is realised by the majority of the potential users. In most cases, limitation is not caused by a lack of the necessary equipment in the laboratories concerned. Thus it remains for the specialists in HPLC to pass on their knowledge to those scientists who have problems with nucleic acid separation but who do not yet have the necessary experience to solve them.

Acknowledgements The stimulating discussions with Dr. U. Aldag are gratefully acknowledged. We thank Ms. H. Gruber for her help in preparing the manuscript. The work from the author’s laboratory was supported by grants from the Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie.

References 1 (a) Grossmann, L. and Moldave, K., eds. (1980) Methods in Enzymology, Vol. 65: Nucleic Acids, Part I. Academic Press, New York and London. (b) Wu, R., ed. (1979) Methods in Enzymology, Vol. 68: Recombinant DNA. Academic Press, New York and London.

104 2 Riesner, D. and Gross, H.J. (1985) Annu. Rev. Biochem. 54, 531-564. 3 Mahy, B.W.J., ed. (1985) Virology - a practical approach. IRL Press, Oxford and Washington. 4 Maniatis, T., Fritsch, E.F. and Shambrock, J. (1982) In: Molecular Cloning, A Laboratory Manual. Cold Spring Harbor Laboratory. 5 Chirikjian, J.C., ed. (1986) Application of Nucleic Acid Probe Technology in Medicine. Elsevier, Amsterdam. 6 Saenger, W. (1984) Principles of Nucleic Acid Structure. Springer-Verlag, New York. 7 Bloomfield, V., Crothers, D. and Tinoco, J., Jr. (1974) Physical Chemistry of Nucleic Acids. Harper and Row, New York. 8 Snyder, L.R. and Kirkland, J.J. (1974) Introduction to Modem Liquid Chromatography. J. Wiley, New York. 9 Engelhardt, H. (1977) Hochdruckfliissigkeitschromatographie.Springer-Verlag, New York. 10 Drager, R.R. and Regnier, F.E. (1985) Anal. Biochem. 145, 47-56. 11 Kato, Y., Nakamura, K. and Hashimoto, T. (1983) J. Chromatogr. 266, 385-394. 12 Pharmacia Catalog (1986) Pharmacia, Uppsala, Sweden. 13 Colpan, M., Schumacher, J., Briiggemann, W., S i g e r , H.L. and Riesner, D. (1983) Anal. Biochem. 131, 257-265. 14 LKB Application Note AP 101. 15 Colpan, M. and Riesner, D., LKB Application Note 357. 16 Colpan, M. and Riesner, D. (1984) J. Chromatogr. 296, 339-353. 17 Cubellis, M.V., Marino, G., Mayol, L., Piccialli, G. and Sannia, G. (1985) J. Chromatogr. 329, 406-414. 18 Colpan, M. and Riesner, D., LKB Application Note 356. 19 NUCLEOGEN DEAE (1986) Diagen, Dusseldorf, F.R.G. 20 Hecker, R., Colpan, M. and Riesner, D. (1985) J. Chromatogr. 326, 251-261. 21 Newton, C.R., Greene, A.R., Heathclifte, G.R., Atkinson, T.C., Holland, D., Markham, A. and Mge, M.D. (1983) Anal. Biochem. 129, 22-30. 22 Zachau, H.G., Tada, M., Lawson, W.B. and Schweiger, M. (1961) Biochim. Biophys. Acta 53, 221. 23 Regnier, F.E. and Gooding, K.M. (1980) Anal. Biochem. 103, 1-25. 24 Simonian, M. and Capp, M.W. (1983) J. Chromatogr. 266, 351-358. 25 Garcia, S. and Liautard, J.-P. (1983) J. Chromatogr. Sci. 21, 398-404. 26 Kelmers, A.D., Novelli, D.G. and Stulberg, M.P. (1965) J. Biol. Chem. 240, 3979. 27 Bischoff, R. and McLauWn, L.W. (1983) J. Chromatogr. 270, 117-126. 28 Bischoff, R., Graeser, E. and McLaughhn, L.W. (1983) J. Chromatogr. 257, 305-315. 29 Larson, J.E., Hardies, S.C., Patient, R.K. and Wells, R.D. (1979) J. Biol. Chem. 254, 5535-5541. 30 Hillen, W., Klein, R.D. and Wells, R.D. (1981) Biochemistry 20, 3748-3756. 31 Wells, R.D., Hardin, S.C., Horn, G.T., Klein, B., Larson, J.E., Neuendorf, S.K., Panagototos, N., Patient, R.K. and Selsing, E. (1980) In: Methods in Enzymology (Grossman, L. and Moldave, K., eds.) Vol. 65, pp. 327-347. Academic Press, New York. 32 Bischoff, R. and McLauWn, L.W. (1984) J. Chromatogr. 296, 329-337. 33 Lehrach, H. and Frischauf, A.M. (1982) EMBL Lett. Manual., EMBL Heidelberg, F.R.G. 34 Gassen, H.G. and Lang, A. (1982) Chemical and Enzymatic Synthesis of Gene Fragments. Verlag Chemie, Weinheim. 35 Tener, G.M. (1967) In: Methods in Enzymology, Vol. 12, (Grossman, L. and Moldave, K., eds.) pp. 398-404, Academic Press, New York. 36 Cook, A.F., De Czekala, A., Gabriel, T.F., Harvey, C.L., Holman, M., Michaelewsky, J.E. and Nussbaum, A.L. (1973) Biochim. Biophys. Acta 324, 433-439. 37 Crea, R., Kraszewski, A., Hirose, T. and Itakura, K. (1978) Proc. Natl. Acad. Sci. USA 75, 5765-5769. 38 Gait, M.J. and Sheppard, R.C. (1977) Nucleic Acids Res. 4, 1135-1158. 39 Fritz, H.-J. Belagaje, R., Brown, E.L., Fritz, R.H., Jones, R.A., Lees, R.G. and Khorana, H.G. (1978) Biochemistry 17,1257-1267. 40 Dizdaroglu, M., Hermes, W., von Sonntag, C. and Schott, H. (1979) J. Chromatogr. 169, 429-435. 41 Dizdaroglu, M. and Hermes, W. (1979) J. Chromatogr. 171, 321-330.

105 42 Aukaty, M.F., Bubenschikova, S.N., Kagrammanova, V.K. and Baratova, L.A. (1977) J. Chromatogr. 137, 351-356. 43 Jost, W. Unger, K.K., Lipecky, R. and Gassen, G. (1979) J. Chromatogr. 185, 403-412. 44 Van Boom, J.H. and De Rooy, J.F,M. (1977) J. Chromatogr. 131, 169-177. 45 Yanagawa, H. (1978) Nucleic Acids Res. Special Publication No. 5, s461-464. 46 Gabriel, T.F. and Michalewsky, J.E. (1973) J. Chromatogr. 80, 263-265. 47 Crowther, J.B., Fazio, S.D. and Hartwick, R.A. (1983) J. Chromatogr. 282, 619-628. 48 McLaughhn, L.W., Cramer, F. and Sprinzl, M. (1981) Anal. Biochem. 112, 60-69. 49 Usher, D.A. (1979) Nucleic Acids Res. 6, 2289-2306. 50 McFarland, G.D. and Borer, P.N. (1979) Nucleic Acids Res. 7, 1067-1080. 51 Walker, G.C., Uhlenbeck, O.C., Bedows, E. and Gumport, R.I. (1975) Proc. Natl. Acad. Sci. USA 72, 122-126. 52 Singhal, R. (1983) J. Chromatogr. 266, 359-383. 53 Rassi, Z.E. and Horvath, C. (1985) J. Chromatogr. 326, 79-90. 54 Anderson, T., Carlsson, M., Hagel, L. and Pernemalm, P.-A. (1985) J. Chromatogr. 326, 33-44. 55 Kato, Y., Sasaki, M. and Hashimoto, T. (1983) J. Chromatogr. 266, 341-349. 56 Graeve, L., Goemann, W., Foldi, P. and Kruppa, J. (1982) Biochem. Biophys. Res. Commun. 107, 1559-1565. 57 Kato, Y., Kitamura, T. and Hashimoto, T. (1984) J. Chromatogr. 292, 418-426. 58 Ogishima, T., Okada, Y. and Omura T. (1984) Anal. Biochem. 138, 309-313. 59 Nguyen, P.N., Bradley, J.L. and McGuire, P.M. (1982) J. Chromatogr. 236, 508-512. 60 Garcia, S. and Liautard, J.P. (1984) J. Chromatogr. 296, 355-362. 61 Shger, H.L., Ramm, K. and Miiller, W., LKB Application Note GF-14A. 62 Kato, Y., Yamasaki, Y. and Hashimoto, T. (1985) J. Chromatogr. 320, 440-444. 63 Kato, Y., Sasaki, M., Hashimoto, T., Murotsu, T., Fukushige, S . and Matsubara, K. (1983) J. Chromatogr. 265, 342-346. 64 Kruppa, J., Graeve, L., Banche, A. and Foldi, P. (1984), LC Magazine 2, 848-853. 65 Dornburg, R., Kruppa, J. and Foldi, P. (1986) LC Magazine 4, 22-29. 66 Colpan, M., Henco, K. and Riesner, D., In preparation. 67 Westerman, E., Skold, S.E. and PernemaLm, P. (1984) 4th Int. Symp. on HPLC of Proteins, Peptides and Polynucleotides, Abstract 308. 68 Pearson, J.D. and Regnier, F.E. (1983) J. Chromatogr. 255, 137-149. 69 Lawson, T.G., Regnier, F.E. and Weith, H.L. (1983) Anal. Biochem. 133, 85-93. 70 Himmel, M., Perna, P.J. and McDonell, M.W. (1982) J. Chromatogr. 240, 155-163. 71 Bohacek, J. and Blazicek, G. (1980) J. Polym. Sci. Polym. Symp. 68, 121-127.

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A. Neuberger and L.L.M. Van Deenen (Eds.) Modern Physical Methodc in Biochemistry, Part B 0 1988

Elsevier Science Publishers B.V. (Biomedical Division)

107

CHAPTER 5

Reversed phase hlgh performance liquid chromatography of peptides and proteins M.T.W. HEARN and M.I. AGUILAR Department of Biochemistry, Monash University, Clayton, Victoria 31 68, Australia

1. Introduction Reversed phase high performance liquid chromatography (RP-HPLC) now plays a critical role in the analysis and purification of peptides and proteins from natural and synthetic sources. The extraordinary popularity of RP-HPLC for polypeptide analysis can be attributed to a number of factors such as: - the excellent resolution which can be achieved for closely related as well as structurally disparate substances under a large variety of chromatographic conditions; - the experimental ease with which chromatographic selectivity can be manipulated through changes in mobile phase composition; - the generally high recoveries, even at ultramicroanalytical levels; - the excellent reproducibility of repetitive separations carried out over long periods of time, due to the stability of the hydrocarbonaceous stationary phase to most mobile phase conditions; - the potential, which is only now beginning to be addressed, for evaluating different physicochemical aspects of solute-eluent or solute-stationary phase interactions from chromatographic data. Some of the potential of RP-HPLC in the purification of polypeptides and proteins is demonstrated by the selected samples summarised in Table 1. Representative of the extremely high resolution which can be obtained with complex samples such as the separation of tryptic peptides is the gradient elution profile of the bovine growth hormone tryptic peptides chromatographed on a 2.1-pm non-porous octadecylsilica stationary phase [l]shown in Fig. 1. Despite the current wide usage of RP-HPLC techniques in protein sequencing studies and many other purification areas involving high resolution polypeptide separations, the selection of a particular chemically-bonded stationary phase and mobile phase composition has frequently been based on empirical criteria. Not uncommonly, such arbitrary

TABLE 1 Selected examples of polypeptides and proteins purified by reversed phase HPLC Polypeptide or protein

Column

Insulin chains P-Cl8 IGF inhibitor Aq-RP Myelin basic protein fragments NP-C,, HLA-I1 H-C,, Growth hormone LS-c, Haemoglobin tryptic peptides Pro-RPC Viral membrane glycoprotein fragments U-RPSC HMG proteins p-CN HMG proteins P-C,, Poliovirus protein B-C,, Flavovirus membrane and capsid proteins U-RPSC Oestrogen synthetase w-P Sendai virus detergent extract V-C,, Nucleoproteins p-CN Nucleoproteins NP-C,, Calmodulin p-AP Myelin basic protein tryptic peptides U-C,, 8-Endorphin fragments U-C,, Parathyroid hormone N-C,, Wheat proteins SY-c,, Interferon and synthetic fragments SY-c,, Sendai virus membrane protein TSK-P Interleukin I fragment P-c,, Heparin-binding growth factors B-C4 8-Casein tryptic peptides A-C, Bacteriophage T4 gene 43 protein tryptic peptides V-C, RBC membrane proteins H-C, Interleukin I1 muteins v-c,

Mobile phase 0.1%formic acid, 0-40% CH,CN, 2.5 ml/min, 6 min 0.1% TFA, 0-45% i-PrOH, 0.7 ml/min, 60 min 0.1% TFA, 5-60% CH,CN, 0.8 ml/min, 30 min 25 m M ammonium bicarbonate, 0-42% CH,CN, 1.9 ml/min, 60 min 100 mM ammonium acetate, 0-60% CH,CN, 1ml/min, 30 min 49 mM KH,PO,, 0-37.5%, CH,CN, 0.7 ml/min, 80 min 0.09% TFA, 0-90%, CH,CN/i-PrOH (1 :l), 2 ml/min, 15 min 0.2% TFA, 0-50% CH,CN, 1 ml/min, 300 min 0.2% TFA, 0-50% CH,CN, 1 ml/min, 300 min 60% formic acid, 10-32% CH,CN, 1 ml/min, 40 min 0.09% TFA, 0-90% CH,CN/i-PrOH (1 :l), 2 ml/min, 15 min 0.1% TFA, 15% CH,CN-100% CH,CN/iPrOH (2: l), 1 ml/min, 30 min 0.1% HCI, 20-65% EtOH/BuOH (4: l), 1 ml/min, 25 min 0.2% TFA, 0-508 CH,CN, 1 ml/min, 300 min 0.2% TFA, 0-50% CH,CN, 1 ml/min, 300 min 10 mM K,HPO,, 2 mM EDTA, 5-65'% CH,CN, 1.5 ml/min, 20 min 0.1% TFA, 0-60% CH,CN, 1 ml/min, 100 min 100 mM NaH,PO,, 16-3556, CH,CN, 1 ml/min, 50 min 10 mM H,PO,-KH,PO,, 10-608, CH,CN, 1 ml/min, 25 min 0.1%TFA, 15-38% CH,CN, 1 ml/min, 42 min 0.25% TFA, 30-60% CH,CN, 2 ml/min, 30 min 0.05% TFA, 15-75% CH,CN, 1 ml/min, 24 min 0.01% TFA, 0-100% CH,CN, 0.8 ml/min, 30 min 0.1% TFA, 0-60% CH,CN, 1ml/min, 90 min 0.1% TFA, 10-50% CH,CN, 0.8 ml/min, 50 min 0.05% TFA, 0-80% CH,CN, 0.7 ml/min, 150 min 0.05% TFA, 0-95% CH,CN, 1 ml/min, 30 min 0.1% TFA, 35-60% CH,CN, 1 ml/min, 40 min

Ref. 64 65 66 67 68 69 70 71 71 72 73 74 75 76 76 77 78 79 80 81 82 83 84 85 86 87 88 89

PDGF-receptor fragments Cholera toxin Endorphin fragments Link protein Insulin receptor kinase Vasoactive intestinal peptide Caerulein Endothelial cell growth factors Atrial natriuretic peptide Gonadotropin-releasing hormone Pyruvate b a s e Anaphylatoxin fragments Enkephalin analogues Histidine decarboxylase fragments Thiolase subunits Tylorrhynchus sp.haemoglobin Tropomyosin tryptic peptides Type IV collagen fragments C-AMP dependent kinase I1 Basic nuclear protein phosphopeptides Mouse salivary gland glycoprotein y-Carboxyglutamic acid protein HMG-CoA synthase Glutathione transferase

v-c, N-C18

sP-c18 ‘-I8

TSK-C,, R-pC18 sp-c ‘-I8

v-c18

0.1% TFA, 8-328 CH,CN/iPrOH (1 : 1) 1 ml/min, 60 min 0.1% TFA, 0-60% CH,CN, 1 ml/min, 98 min 0.1% TFA, 0-50% CH,CN, 1 ml/min, 20 min 0.1% TFA, 0-5051; CH,CN, 1 ml/min, 100 min 0.05% TFA, 0-100% CH,CN, 0.8 ml/min, 0.1%TFA, 0-50% CH,CN, 1 ml/min, 50 min 0.1%TFA, 0-602 CH,CN, 1.5 ml/min, 60 min 0.1% TFA, 20-50% CH,CN, 10 ml/min, 60 min 0.1% TFA, 0-3756 CH,CN, 1 ml/min, 22 min 0.1% TFA, 0-50% CH,CN, 1 ml/min, 50 min 0.1% TFA, 0-30% CH,CN, 1 ml/min, 120 min 0.1% TFA, pH 3.5, (ammonium hydroxide), 5-95% CH,CN, 1 ml/min, 40 min 35 mM ammonium acetate, 30-80% CH,CN, 1 ml/min, 30 min 0.1% TFA, 0-80% CH,CN, 1 ml/min, 40 min 0.0551; TFA, 35-502 CH,CN, 1 ml/min, 30 min 50 mM ammonium bicarbonate, 0-50% CH,CN, 1 ml/min, 100 min 0.05% TFA, 0-508 CH,CN, 1 ml/min, 50 min 0.1% TFA, 31-39% CH,CN, 1.2 ml/min, 48 min 0.1% TFA, 0-408 CH,CN, 1 ml/min, 140 min 0.1% TFA, 0-10% CH,CN, 1.5 ml/min, 10 min 0.1% TFA, 0-100% CH,OH, 1ml/min, 60 min 0.1% TFA, 0-40% CH,CN, 1 ml/min, 60 min 0.1% TFA, 0-60% CH,CN, 1 ml/min, 40 min 0.1% TFA, 0-60 CH,CN, 1 ml/min, 40 min

90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

p-C,, = p-Bondapak C,,; Aq-RP = Aquapore-RP-C,,; NP-C,, = Novapak-C,,; H-C,, = Hypersil ODs; LS-C, = N-butyl Lichrosphere-500; Pro-RPC = Pharmacia RP-C,,;U-RPSC = Ultrapore RPSC-C,; p-CN = p Bondapak CN; B-C,, = Bakerbond Wide Pore C,,; W-P = Whatman Proteosil 300 Diphenyl; V-C,, = Vydac 218 TP-C,,; p-AP = p Bondapak-alkylphenyl; U-C,, = Ultrasphere-ODs; N-C,, = Nucleosil-C,,; Sy-C,, = Synchropak RP-P Cl,; TSK-P = Toyasoda TSK 5PW-Phenyl; B-C, = Bakerbond Wide Pore C,; A-C,, = Apex C,,; V-C, = Vydac 214 TPC,; H-C, = Hibore R-304, C,; V-C, = Vydac RP-300 C,; Nucleosil C,,; Sp-C,,, Sperisorb ODs-2; TSK-C,, = Utropac TSK ODs; R-pC,, = Radial pak, p Bondapak M-C,, = Micropak MCH-C,,, Partisil-5, ODs-3; Z-C,,, Zorbax ODs; LS-C, = Li Chrosorb RP-8; Li-C,, = LiChrosphere RP-18 I-CN = IBM CN; TFA = trifluoroacetic acid.

ii 0

15

30

45

60

Time (min)

Fig. 1. Elution profile of a tryptic digest of bovine growth hormone on a C,, non-porous silica column, particle diameter 2.1 p m (3.6 c m x 8 mm ID). Gradient from 0-50% acetonitrile in 0.1%TFA in 60 min at a flow rate of 1 ml/min.

selections may not adequately address the issues of optimal chromatographic resolution, band shape or solute recovery. Clearly more information on stationary phase topography and the physicochemical basis of polypeptide retention in reversed phase systems is required before these empirical approaches can be replaced by systematic strategies for optimising resolution and recoveries. In several investigations [2-lo], the influence of mobile phase composition on the chromatographic behaviour of polypeptides separated on chemically bonded n-alkylsilicas has been documented. Other studies [ll-161 have examined the effect of stationary phase characteristics, including the particle size, the mean pore diameter, the porosity, the accessible surface area, the ligand composition and surface density on polypeptide resolution and recovery in RP-HPLC systems. Indeed, the extensive compilation by Unger [17] of the properties and use of silica in column liquid chromatography provides a detailed assessment of several hundred types of packing currently available. Column configuration [6,11], mobile phase flow rate [2,6], temperature [3] and sample size [18] are also known to affect resolution and recovery - two crucial aspects of a successful purification (the thrd being separation speed). The overwhelming conclusion which can be drawn from numerous investigations over the past few years is that the separation of polypeptides on n-alkylsilicas involves chromatographic distribution and kinetic phenomena which are much more complex than those shown by small polar molecules. These differences in polypeptide chromatographic behaviour in reversed phase systems are now known to be due to composite effects arising from: (1) specific solute-solvation equilibria [9], (2)

111

multisite interaction with the heterogeneous stationary phase surface [8], (3) solute aggregation in the bulk mobile phase or at the stationary phase surface [20], (4) sol-gel equilibria [21], (5) specific ion-interaction equilibria involving ionic additives present in the mobile phase or adsorbed on the non-polar stationary phase surface [22] and (6) specific pH-dependent ionisation equilibria [22] which reflect the unique isoelectric point characteristics of these zwitterionic polyelectrolytes in solution. Systematic evaluation of the composite interplay of these various phenomena currently presents a, major intellectual and experimental challenge to the peptide chemist and the chromatographer alike as they search for rational, predictive approaches to obviate the inherent complexities of optimising resolution whilst concurrently decreasing separation time and improving overall mass recovery. Although solutions to some of these issues have been derived from the classical age of chromatographic theory and practice, considerable gaps still exist in knowledge of the underlying mechanisms which control retention, band-broadening and recovery. For example, the dynamic effect of conformational equilibria [23] established by polypeptides and proteins in the bulk mobile phase and at the stationary phase surface remain poorly understood. Furthermore, current predictive procedures for the optimisation of chromatographic conditions largely rely on empirical approaches, and rarely involve stochastic approaches which ultimately require validation through analysis of a series of chromatographic experiments based on variation of peak capacities. Although these approaches may even involve computer-aided design of the mobile phase composition, temperature, or pH or manipulation of experimental hardware such as the stationary phase particle diameter, they all make the same fundamental assumption that the three-dimensional structure of the solute is condition independent. This clearly is not the case. Ideally, chromatographic optimisation should be based on quantitative structure-retention relationships. However, such fully developed mechanistic approaches are still very much in their infancy for polypeptides and proteins due to their complex structures and their propensity to undergo conformational reorientation both in solution and during their interaction with synthetic surfaces. Recent advances in the theoretical basis and the experimental design with high performance chromatographic systems now enable evaluations to be made of different physicochemical aspects of solute-eluent and solute-stationary phase interactions from chromatographic data. This chapter therefore documents recent theoretical developments whch characterise the RP-HPLC of polypeptides and proteins, and describes recent advances in the evolution of fully mechanistic models which describe in physicochemical terms the nature of the interaction between biological macromolecules and biological and synthetic surfaces.

2. Retention relationships of peptides in RP-HPLC The growth in the number of applications of RP-HPLC in peptide and protein purification has far outstripped the rate of development of fully mechanistic models which adequately describe the underlying thermodynamic and kinetic processes

112

involved in the interaction of peptide solutes with non-polar stationary phases. It is evident from the relevant literature that far from optimal resolution, peak shape and recovery of polypeptides and proteins are often obtained. In the absence of rigorous models capable of predicting retention and bandwidth dependencies on experimental conditions, there has been little recourse for investigators but to change experimental parameters arbitrarily, often with only a few trial-and-error guidelines for success. Several investigations have now been reported [4,8,24-261 which describe predictive, non-mechanistic optimisation models for the isocratic and gradient elution of peptide solutes by RP-HPLC. For example, the capacity factor, k ’ , of a polypeptide separated by reversed phase isocratic elution has been expressed as a linear function of organic volume faction, $J, such that over a defined range of A+ values, log k’

= log

k; - S$J

(1)

Depending on the magnitude of the S and log k ; parameters a variety of dependencies of solute retention on mobile phase eluotropic strength can be calculated as depicted in Fig. 2. Cases (c) and (d) in Fig. 2 represent typical scenaria for the RP-HPLC of highly hydrophobic polypeptides and globular proteins, whilst cases (a) and (b) are more representative of the RP-HPLC behaviour of polar peptides and small polar globular proteins. Plots of log k’ versus $J for polypeptides separated on n-alkylsilicas are generally found from experimental studies to be curved rather than linear. Examples of the plots of experimental logarithmic capacity factors k ‘ , against organic solvent strength for several hormonal polypeptides [2] are shown in Fig. 3. In cases such as these, the tangent, S , to the log k’ versus $I curve can be calculated at a particular value of k’ and the value of log k’ at = 0 (log kb) obtained by extrapolation using linear or non-linear regression analysis. The S values and log k; values of polypeptides and proteins are usually large when compared to those of simple organic molecules. This feature of polypeptide retention behaviour on n-alkylsilicas is believed to be a consequence of multisite ligand-solute interactions and is a reflection of the magnitude of the hydrophobic contact area established between the solute and the hydrocarbonaceous ligand. Evaluation of S and log k; values is important for several reasons. First, this information can be directly applied to the enhancement of resolution via optimisation procedures with a particular chromatographic system through the determination of resolution as follows

+

where N is the separation efficiency and the selectivity, a, between the two solutes

P, and P2, i.e. k;/k,‘ is determined by

113

0

5 Fig. 2. Schematic representation of the retention dependencies for peptides or proteins chromatographed on mixed-mode support media. The figure illustrates four case histories for the dependency of the logarithmic capacity factor (log k ' ) on the mole fraction, {, of the displacing species. As the contact area associated with the solute-ligand interaction increases, the slopes of the log k' versus { plots increase resulting in a narrowing of the elution window over which the solute will desorb. Cases (a) and (b) are typically observed for the RP-HPLC of polar peptides and small, polar globular proteins whilst cases (c) and (d) are more representative of the RP-HPLC behaviour of highly hydrophobic polypeptides and non-polar globular proteins, respectively.

These relationships provide the basis of iterative computational assessment of microprocessor-controlled approaches to the optimisation of chromatographic selectivity using a number of resolution protocols including simultaneous, sequential, factorial or interpretative methods for the analysis of chromatographic data [27]. Secondly, knowledge of the S and log k' values greatly simplifies the determination of physicochemical relationships underlying selectivity-functional group dependencies. The chromatographic behaviour and biological activity of a peptide are closely dependent on its three-dimensional structure, and the application of the above expressions and derived algorithms allows quantitative structure-activity relationships to be correlated with chromatographic retention data via linear free-energy relationships [10,28,29]. Chromatograpkc selectivity increments (7)can therefore be formally related to functional coefficients through expressions such as log a = 7 = f ( K )

(4)

114

32

18 61 80 ACETONITRILE Fig. 3. Plots of the logarithmic capacity factors for hen lysozyme and several hormonal polypeptides against the volume fraction, 4 of the organic solvent in water-acetonitrile isocratic mobile phases. Conditions: Column, p-Bondapak C18; flow-rate, 2.0 ml/min; primary mobile phases, (a) water - 4 mM sodium sulphate-15 mM orthophosphoric acid, pH 2.2, and (b) water - 4 mM sulphuric acid-15 mM orthophosphoric acid-15 mM triethylamine with the acetonitrile content adjusted over the 4 range 0.0-0.8.The polypeptide key is; 1= hen lysozyme; 2 = porcine glucagon; 3 =bovine insulin; 4 = bovine insulin p chain; 5 = arginine vasopressin; 6 = lysine vasopressin. From [2]. 16

*/a

where K is a measure of biological function. Thirdly, analysis of these chromatographic variables provides quantitative guidelines required for the preparation of improved hydrophobic microparticulate stationary phases through the characterisation of different stationary phase topographies and the effect of different column configurations. The determination of S and log k; values for a large variety of polypeptides and proteins encompassing differences in composition, sequence, size and hydrophobicity can be derived from isocratic chromatographic data but these measurements are time consuming and require high experimental precision. Furthermore, many polypeptides and proteins exhibit skewed peaks when eluted under isocratic conditions from n-alkylsilicas and, as a consequence, accurate determination of the average elution time and the peak variance requires calculation of the first and second moments of the peak zone. Although isocratic conditions can in many instances be employed in the separation of different polypeptides under well-defined reversed phase conditions, complex mixtures of peptides and proteins are now typically separated on n-alkylsilicas under gradient elution conditions. Recently, several studies on the development of optimisation models for the isocratic and gradient elution separation of low and high molecular weight solutes by RP-HPLC have been

115

described [4,12,24,25]. In particular, concepts derived from the linear solvent strength (LSS) gradient model [4,6,9,10] have been shown to provide a useful basis for evaluating the retention behaviour of polypeptides and proteins separated under regular reversed phase systems. Gradient elution therefore represents a logical alternative to reduce separation times, decrease peak volume and to further characterise the physicochemical basis of polypeptide retention in RP-HPLC. If it is assumed that the same chromatographic variables which control retention, resolution and bandwidth in isocratic elution are also relevant in gradient elution, then solute S and log k ; values can be determined through the application of the LSS theory. It has been shown [24] that the retention time, t,, for a polypeptide chromatographed under gradient elution conditions with a binary gradient from solvent A to solvent B can be related to the gradient steepness parameter, b, through the expression

where to is the column dead time and t , is the gradient elapse time required for the change in solvent B to reach the column inlet. The determination of b values can be easily achieved by using different gradient times or flow rates. Thus, when solutes are chromatographed over a range of gradient times in the same column with the same mobile phase system, the gradient steepness parameter can be derived by using the relationship

where t,, and t are the gradient retention times of the solute at gradient times tG1 92. and tG2,respectively, and the coefficient P represents the ratio of the respective gradient times ( = tG,/tGl). In the case of solutes chromatographed under linear solvent strength gradient conditions at two different flow rates, F, and F2, the b value can be determined from the following expression

where X ,

=

t,, - to,, to,,

and X 2 =

t,2

- t0,2 t0.2

Evaluation of the b values from retention data determined over various - gradient times allows the calculation of a range of median capacity factors, k and the corresponding organic mole fraction 6 according to -

k = 1/1.15b and

(8)

116

M

-0.2

!

I

I

I

I

I

I

0

01

02

o.J

04

M

i

z

Fig. 4. Plots of log versus 6 based on gradient experiments for P-endorphn-related peptides 7, 8, 10, 11, 14-16. The plots were derived from best-fit analysis to the data points obtained from gradient elution experiments, where tG = 20, 30, 40, 60 and 120 min and F=1 ml/min. Column, developmental octadecylsilica, d, = 6 pm, pd = 13 nm, 25 cm X4.6 mm ID. Solvent A, 0.1% trifluoroacetic acid (TFA) in water; solvent B, 0.1% TFA in water-acetonitrile (50:50). See Table 2 for the code to polypeptide structure and for the calculated slope parameter S and log kh values. Note the changes in band spacing for peptides 7, 8, 10 and 11 which illustrate the potential for selectivity manipulation through changes in the gradient steepness parameter, b. From [4].

6

where t g = tG,/A+. These values of k and are formally equivalent to the isocratic parameters k’ and @I and can therefore be related by analogy with equation (1) through the empirical expression

6

The tangent S to the curve obtained in a plot of log k versus such as the data illustrated in Fig. 4 for the P-endorphin analogues can thus be determined at any particular value of k and the values of log k at @I = 0, or log k ; , can be obtained by extrapolation using regression analysis. The values of S and log k i derived in this manner are listed in Table 2 for a variety of peptides and proteins encompassing a wide range of molecular characteristics. It has been shown that changes in retention processes which are mediated through different classes of binding sites on the heterogeneous stationary phase

117 TABLE 2 Structure and retention parameters of polypeptides and proteins PEPTIOE

SEQUENCE

* l o g k',

MW

S

Endorphin Analogues 1. YGGFM 2. YGGFMTS 3. YGGFMTSEKSQTPLVT 4. YGGFMTSEKSQTPLVTL 5. YGGFMTSEKSOTPLVTLFK 6. YGGFMTSEKS~TPLVTLFKNAI IKNAYKKGE 7. GGFM 8. GGFMT 9. GGFMTS GGFMTSE 10. GGFMTSEK 11. 12. GGFMTSEKSO GGFMTSEKS~TP 13. 14. GGFMTSEKSQTPLVT 15. GGFMTSEKSQTPLVTL 16. GGFMTSEKSQTPLVTLF 17. GGFMTSEKSQTPLVTLFK 18. TSEK 19. MTSEK FMTSEK 20. IIKNAYKKGE 21. FKNAIIKNAYKKGE 22. LVTL 23. SQTPLVTL 24. KSQTPLVTL 25. EKSQTPLVTL 26. SEKSQTPLVTL 21. TSEKSQTPLVTL 28. MTSEKSQTPLVTL 29.

573 161 1744 1859 2134 3263 410 511 598 727 855 1010 1268 1581 1694 1841 1969 463 594 141 1162 1622 444 857 985 1114 1201 1302 1433

10.0 11.2 14.2 13.1 13.1 15.1 9.0 9.7 14.6 11.6 10.9 13.3 14.3 15.2 13.1 12.8 14.0 20.0 13.3 15.8 15.8 10.8 13.7 13.1 13.4 13.9 14.0 14.2

3.8 5.6 6.9 9.9 7.1 9.2 9.0 9.4

L u t e i n i z i n g Hormone R e l e a s i n g Hormone Analogues 1. CEH-OCH3 2. <EHW 3. <EHWS 4. <EHWSY 5. GLRPG-NH 6. ~EHWSYGLRPG-NH:

298 410 551 723 583 1216

63.1 11.9 13.5 14.3 19.0 18.6

-0.2 1.8 1.6 2.6 1.4 3.6

Growth Hormone R e l e a s i n g F a c t o r Analogues 1. QQGERNQE-NH 2. RQQGERNQE-NH~ 3. IMNRQQGERNQE-NH:

985 1141 1499

29.3 29.4 24.1

0.9 1.1 1.7

Myosin R e l a t e d P e p t i d e s 1. KKRAAARTSNVFA 2. KKRAARATSNVFA 3. KKRARAATSNVFA 4. KKRRAAATSNVFA 5. AKRPQRATSNVFS 6. KARPQRATSNVFS 7. KKAPQRATSNVFS 8. KKRARATSNVFA 9. KKRAAARATSNVFA 10. KKRAAAARATSNVFA

1418 1418 1418 1418 1460 1460 1444 1347 1489 1560

15.3 15.3 15.4 15.5 15.8 15.7 15.5 15.4 16.0 16.8

2.2 2.1 2.2 2.3 2.3 2.2 2.2 2.2 2.4 2.5

883 911 925 953 995

19.2 17.2 15.6 16.8 14.5

1.5 1.6 1.6 2.1 2.2

600 630 1300 3500

11.3 12.8 15.2 22.3 22.7 41.3 39.2

3.2 3.4 4.7 8.1 7.9 12.3 15.4

Hodges' Standard P e p t i d e s 1. RGAGGLGLGK-NH2 2. Ac-RGGGGLGLGK-NH2 3. Ac-RGAGGLGLGK-NH AC-RGVGGLGLGK-NH~ 4. 5. A~-RGVVGLGLGK-NH: Data from Reference 6 1. Leu-Enkephalin 2. Bradykinin 3. Angi o t e n s i n 4. G1 ucagon 5. Insulin 6. R i bonuclease A 7. Lysozyme

Table 2 continued on next page.

6000

12500 14000

1.3 7.7 11.4 12.6 14.1 18.6 5.7 5.8 6.6 5.5 5.8 7.0

8.3 11.0 12.1 13.6 14.2

9.6

9.4 9.7

118 TABLE 2, continued Chromatographic conditions were as follows: Endorphin analogues: developmental CIS,6 pm, 13 nm, 25 cmx4.5 mm ID; 0.1% TFA, 0-50% CH3CN , tG = 20-120 min, flow = 1 - 4 ml/min. LHRH, GHRF and myosin analogues. Bakerbond Wide Pore, C,, 5 pm, 30 nm, 25 cmx4.6 mm ID; 0.1% TFA, 0-50% CH,CN, tG = 20-120 min, flow =1-4 ml/min. Standard peptides; Synchropak RP-P CIS, 6.5 pm, 30 nm, 25 cmX 10 mm ID; 0.05/0.1% TFA, O-lOO% CH,CN, tG = 25-200 min, flow = 0.3-5 ml/min. Protein [6],developmental C,, 5 pm, 15 nm, 8.0 cmX6.2 mm ID; 0.1% morpholine/O.l25% TFA, 5-458 CH3CN, tG = 10-60 min, flow = 1-4 ml/min. * Data compiled from Hearn et al. [4,9,10,47].

surface or through different topographic regions of the exposed solvated surface structure of the solute lead to different values of S for the compounds in question. Subtle differences in experimentally observed S values for several classes of peptide analogues related to P-endorphin [4], myosin light chain [lo], leuteinising hormone releasing hormone (LHRH) [9], growth hormone releasing factor (GHRF) [9] and interleukin-2 (IL-2) muteins [30] have been reported which reflect the differences within each group in the interactive sites on the peptide solute. Fig. 5 shows the plots of log k versus 6 for the myosin kinase substrate analogues [lo]. Even with this set of closely-related peptides in which only minor differences in the amino acid compositions and sequences occur (e.g. peptide (1) = KKRAAARTSNVFA and peptide (4) = KKRRAAATSNVFA) it is evident that selectivity changes occur over the range of experimental conditions employed. Clearly, for solute analogues where exactly the same molecular region is involved in the interaction with the stationary phase surface through specific orientation of preferred conformers, coincidental retention behaviour with parallelism in the log k versus 6 plots will arise. When these cases are anticipated for two closely related analogues, modulation of selectivity can be achieved through manipulation of secondary solution equilibria such as pH or ion pairing effects. For detailed discussion of the role of ion-pairing phenomena in the RP-HPLC of peptides see [22]. In several studies [4,6,9,10], empirical relationships which link S values and molecular weight (MW) of a polypeptide have been derived in the form

where the coefficients a and b have varied according to the set of peptides and chromatographic conditions. The value of the parameter S in reversed phase separations of polypeptides and proteins is related to the magnitude of the hydrophobic contact area and the number of interaction sites established between the solute and the stationary phase ligands during the adsorption process. Although these sites could increase in number with increasing molecular weight and size of the solute, it will not be the molecular weight per se but rather the polarity and spatial disposition of the surface amino acid residues involved in the interaction with the stationary phase which will ultimately control the mechanistic pathway of the binding process. Therefore, if the peptide assumes any degree of preferred folding, no simple relationship will exist between S and molecular weight or indeed the

119

1.0

0-8

06

IS

04

m

0

.02

0

-0 2 - 0.4 006

0.08

040

0.12

014

0.16

8 x

Fig. 5. Plots of log versus 6 based on gradient experiments for myosin-related peptides 1-10. The plots were derived from best-fit analysis to the data points (which have been excluded for clarity), where tG = 20, 30, 40, 60 and 120 min and flow =1, 2, 3 and 4 ml/min. Column, Bakerbond Wide Pore C4, d, = 5 pm, pd = 30 nm, 25 cmX4.6 mm ID. Solvent A, 0.1% TFA in water; solvent B, 0.1% TFA in water-acetonitrile (50: 50). See Table 2 for the code to peptide structure and for the derived S and log kh values. Note the changes in band-spacing observed for all peptides which demonstrate the potential for selectivity optimisation of very closely related peptides through changes in the gradient steepness parameter. b. From [lo].

summated hydrophobicity coefficients E x nf, calculated according to the linear amino acid sequence. Since the magnitude of log k ; is a measure of the free energy changes associated with the binding of the solute to the stationary phase under the initial gradient conditions, it could be anticipated that log k ; values should progressively increase with incremental increases in solute hydrophobicity. With small peptide oligomers such as polyalanine or polyphenylalanine incremental increases in log k ; have been observed. Furthermore, a linearised relationship between isocratic log k ’ or gradient

120

log k and relative hydrophobicity Zx,, f, of the peptide solute forms the basis of chromatographic methods to determine hydrophobicity coefficients of individual amino acid residues. The prediction of peptide retention times using these hydrophobicity scales assumes that the chromatographic behaviour of these solutes can be characterised in terms of small molecule theory. While t h s assumption may not be well founded in most cases, this approach represents a practical method in the initial stages of chromatographic optimisation procedures.

3. The relationship between peptide retention behaviour and hydrophobicity coefficients The mechanism by which peptide solutes are retained in RP-HPLC depends on the hydrophobic expulsion of the ionised peptidic solutes from polar mobile phases with concomitant adsorption onto the surface of a non-polar stationary phase. Under these conditions, peptides are retarded to different extents depending on their intrinsic hydrophobicities, the eluotropicity of the mobile phase and the nature of the hydrocarbonaceous stationary phase. In order to accommodate the great structural diversity which peptides can exhibit, a large variety of mobile phase combinations has been developed. As discussed in the previous section, optimisation of peptide retention can be achieved by suitable manipulation of mobile phase conditions through changes in organic solvent composition or secondary chemical equilibria such as ionisation, pairing ion and solvation effects. It is now clearly apparent that the nature of the ionised centres of the amino acid side chains have dominant influences on the retention behaviour of peptides with alkylsilicas under elution conditions which involve aquo-organic solvent mobile phases in the pH range 2.0-7.0. Furthermore, the concept that solute structure may be quantitatively related to chromatographic retention assumes that retention behavioural differences can be evaluated from topographical parameters which accommodate the influence of amino acid side chain and group contributions in the retention process. Considerable success has been achieved in the prediction of retention behaviour of neutral and polar solutes, such as benzene derivatives and weak organic acids and bases, separated on reversed phases from quantitative estimates of solute hydrophobicities. In many cases, these estimates were based on topographical indices such as the Hansch 7~ constants derived from classical n-octanol/ water partition coefficients or related incremental parameters. With homologous peptides it has been noted that the retention behaviour appears to follow that predicted on the basis of the summated hydrophobic contribution from each amino acid side chain. For example, a linear dependency was observed 1341 between log k' and the number (n) of residues for alanine oligomers. In most earlier studies 135-441, the procedures used to derive individual amino acid group retention contribution values have been based on repetitive regression analysis associated with forcing procedures or by mathematical routines €or solving linear equations. In the latter approach 1351, peptides

121

with observed retention times and known amino acid compositions are listed as a series of simultaneous equations in the form

[

[

]I![

whch can be rewritten in matrix form as follow

A=

--amlam2

---

Qmn

xl]b=

Xn

A solution to the multiple linear equation is obtained by the method of least squares with Gaussian fitting of the variance. The basis of these calculations assumes that peptide retention can be described solely in terms of ideal reversed phase behaviour. Thus in the absence of electrostatic or hydrogen bonding effects, the solute retention will be determined solely by the nature of the solvophobic solute-ligand interaction and is given in terms of the capacity factor k' according to

k,'

= @Ki

(15)

where K , is the equilibrium association constant and @ is the phase ratio, (volume stationary phase)/(volume mobile phase). Column selectivity between two peptides, P, and P, and then be expressed as In a,,,= In( k;/k,')

(16)

If we consider two peptides of similar sequence differing only by one amino acid residue, then the group retention contribution 7 or chromatographic selectivity increment, due to the different amino acid can be defined as

The 7 contribution is thus a function of the differences in the overall standard unitary free energy changes and can be formally associated with the transfer of the peptide solute (1) from the mobile phase to the stationary phase relative to the transfer of a polyglycine analogue of identical residue number. According to the solvophobic theory [46], the surface area, A A , , of the solute molecule in contact with the non-polar stationary phase plays a significant role in determining the magnitude of the hydrophobic interaction. Since linear free energy relationships are anticipated between bulk phase partition parameters and functional group contributions, h e a r relationships should exist between retention behaviour, as expressed by

122

1.2

-

1.0

c

E

0.8

Y

-

0.6

0

1

0.4

-0 2

0

0.2

0.4

c Fig. 6 . Plots of the logarithms of the reciprocal of the activity coefficient for phosphorylation by myosin light-chain kinase versus the functional group T values for the various myosin light-chain peptide analogues 1-10. Also shown are the regression lines for these peptides, grouped according to their sequential arrangement, as derived from the relationship [log K,,,-'= e7 +d. The point T = 0 corresponds to peptide 2. See Table 2 for the code to peptide structure and legend to Fig. 5 for chromatographic details. From [lo].

In k' (or In k) values and the hydrocarbonaceous surface areas of the solutes. For example, the dependence of the activity coefficient, K,, for the phosphorylation of ten myosin-related analogues on the extrathermodynamic functional group effect, T , was assessed [lo] according to the linearised expression [log K m ] - ' = e T + d Plots of [log K,]-' versus T similar to those in Fig. 6 can provide a basis to evaluate quantitative structure-activity relationships of polypeptides in terms of constitutional and environmental factors. While the utility of the LSS retention model in the optimisation of the resolution of peptide mixtures has been well established, a number of chromatographc experiments is required to determine the S and log k; values. Several studies have now been reported which describe the derivation of retention coefficient scales to measure the contribution of each amino acid residue to the overall retention of a particular peptide. Using these scales, the retention time on a particular reversed phase support of a peptide of known amino acid composition can be predicted relative to a standard which, in principle, obviates the requirement for several preliminary chromatographic experiments to be performed. Various amino acid hydrophobicity coefficient scales derived from both chromatographic and octanol-water partition studies are listed in Table 3. Comparison of the experimentally observed retention times with those predicted from the summated hydrophobicity coefficients suggests that these approaches can in some special circumstances provide a reasonably accurate estimation of the elution profile

123

of a closely related set of peptides (i.e. phenylalanine oligomers) in the particular solvent system in which the coefficients were originally derived. However, divergencies between the experimental and predicted data have been observed with other peptide analogues which may be due to a number of factors. For example, the 2x,f, calculations do not account for differences in specific electrostatic and hydrogen-bonding interactions which are known to arise during the distribution of ionised peptides between polar mobile phases and hydrocarbonaceous silicas. The heterogeneity of the stationary phase surface of alkyl-bonded silicas has been examined in detail, and even with well ‘end-capped’ alkylsilicas of high carbon coverage, unprotected peptides show dual retention behaviour typified by the concave bimodal dependence of In k’ on the volume fraction of water in the mobile phase. This dual retention behaviour has been attributed to composite solvophobic-silanophilic interactions. In addition, specific solvation effects dependent on the nature and concentration of the organic solvent modifier can lead to individual selectivity divergencies for some peptides. Furthermore, in studies where gradient elution was used to derive the relative hydrophobicity scales [45],it is

10

120 MlNS

IY 5

24

i

21

0 0

5

10

15

20

Fig. 7. Plots of k versus summated peptide hydrophobicity Bx calculated according to [36] at two different gradient times tG = 40 and 120 min for P-endorphin-related analogues 1-29. See Table 2 for code to peptide structure and legend to Fig. 4 for other chromatographic conditions. From [4].

TABLE 3 Hydrophobicity group retention contribution for amino acid residues Amino acid Asp Asn Thr Ser Glu Gln Pro GlY Ala CYS Val Met Ile Leu S r Phe His

x1 1.92

- 1.76 - 0.79

0.66 0.44 - 0.76 - 0.40 - 0.82 -0.12 - 1.25 1.08 3.56 5.80 3.16 - 0.79 2.52 - 2.67 LYS -0.53 A% - 1.37 Trp - 0.28 End groups 1.54 Amide -

x2

x3

x4

-0.02 - 1.05 - 0.26 - 0.56 - 0.07 - 1.09 1.01 0.00 0.53 0.93 1.46 1.08 1.99 1.99 1.70 2.24 - 0.23 0.52 - 1.10 2.31

- 1.6

-0.17 - 0.40 0.39 0.05 0.28 0.05 0.56 0.00 0.37 0.69 1.13 1.39 1.58 1.58 1.70 1.83 - 1.30 - 0.87 - 1.23 1.87

- 4.2

- 1.7 - 3.2

1.1 - 2.0

-

3.1 0.2 1.o 4.6 4.6 4.0 7.0 9.6 6.7 12.6 - 2.2 - 3.0 - 2.0 15.1 2.5

-

-

xs -

-1.5 0.5 -0.5 -

-1.0 1.5 0.0 1.0 -

3.0 2.5 3.5 5.O 4.5 5.0 1.0

-

6.5

-

-

-

-

x6

x7

- 1.4 -0.2 -2.2 -0.6 0.0 -0.2 2.2 1.2 -0.3 6.3 5.9 2.5 4.3 6.6 7.1 7.5 -1.3 3.6 - 1.1 7.9

- 2.9

- 2.8

0

-

- 5.7

- 2.8

-

-

-

0.8

XS

400

-

- 300

-

- 1.5

0

-

1.8 5.6 - 2.3 3.9 - 14.3 2.1 4.1 11.0 15.0 3.8 14.7 2.0 - 2.5 3.2 17.8 6.6 8.1

-

-

1.1

- 4.1

- 3.5

- 7.1 - 0.3

5.1 - 1.2 7.3 - 9.2 3.5 5.6 6.6 20.0 5.9 19.2 - 2.1 - 3.7 - 3.6 16.3 6.6 10.3

XI0

x9

2 600 0 500

1500 1300 2 950 1800 2 300 2 500 500 1500 750 3400

-

- 3.03

- 2.94 -

- 2.10 -

- 1.71 - 2.26 - 1.43 - 2.86 - 2.82

- 2.59 - 1.04 -

XI1

0.10 0.45 0.12 0.18 0.27 0.36 0.48 0.22 0.13

XI2

0.2

- 0.6

XI3

- 2.6 - 0.8

0.6

0.3

- 0.2

- 0.5 - 1.3

-

1.1 0.0 2.0 - 0.2 2.0 2.6 5.0 5.5 7.4 8.1 4.5 8.1 - 2.1 - 2.1 - 0.6 8.8 - 7.7

-

-

0.38 0.85 1.38 1.34 1.23 1.71 0.34 0.05 0.26 2.34

0.0 2.2 - 0.2 2.2 2.6 5.1 6.0 8.3 9.0 4.6 9.0 2.2 - 0.2 0.9 9.5 - 7.6 -

The hydrophobicity group coefficients xz, x4, xs, x9 and xlo [36,38,39,42 and 43, respectively] were derived from classical partition studies. The hydrophobicity group coefficient x1 values [35] were obtained by mathematical routines for solving linear equations derived from chromatographic retention data using a Na H2P0,-based mobile phase. x3, x6, x7, xs and xl, [37,40,41,44] were derived by repetitive regression analysis with forcing procedures using chromatographic data in the NaCIO,, trifluoroacetic acid (TFA) ( x s and x7),heptafluorobutyric acid and TFA, respectively. xI2and xI3values [45] were determined by measuring the effect of substitution of each amino acid residue on the retention of a model synthetic peptide in TFA and NaCIO,/(NH,), HPO, based mobile phases, respectively.

125

1.2

1.0

05

04

I*

-

P 0

04

0.2

0

-0.2

- 0.4 0

I

I

I

I

0.05

0.1

0.15

02

6 Fig. 8. Plots of log versus 5 based on gradient elution chromatography of LHRH-related peptides 2-6. The plots were derived from best-fit analysis to the data points shown where t , = 20, 30, 40, 60 and 120 min and F = 1 ml/min (0) and F = 1, 2, 3 and 4 ml/min and tG = 40 (0).Column, Bakerbond Wide Pore C,, d, = 5 pm, pd = 30 nm. Solvent A, 0.1%TFA in water, solvent B, 0.1%TFA in water-acetonitrile (50: 50). See Table 2 for the code to peptide structure and the derived S and log k& values. From [9].

assumed that S values are constant for all solutes. As is evident from Fig. 7 and other recent studies [4,9,10]on the gradient elution behaviour of different classes of peptides this assumption must be seriously questioned even for small peptides of less than 20 residues. For example Fig. 7 shows data comparing the observed and calculated gradient retention for a group of P-endorphin related peptides. If k’ (experimental) values correlated precisely with k ’ (calculated from X-coefficients) values then a straight line with slope of unity would be anticipated for gradients of different development time. As the data indicate, significant divergencies occur from this idealised correlation. The question then is ‘What is the origin of this dichotomy?’. Several other examples exist of peptides [4,10,14,47]such as the retention behaviour observed for the LHRH-related peptides shown in Fig. 8 whose sequence contains preferential interaction sites which were not necessarily apparent from initial inspection of the amino acid sequence, but become clearly evident after

126

subsequent analysis of the retention and bandwidth data. These studies have demonstrated that differences in retention time within a series of peptide analogues can only be related to the changes in amino acid composition ;f the site of interaction with the stationary phase surface is identical for all peptides and that the substituted amino acids are located in the interactive section of .ne peptide. While the hydrophobic group retention contributions of the amino acid residues in small peptides have an essentially additive effect on peptide retention to alkylsilicas and can be used to provide approximate elution order with peptides of known amino acid composition, a detailed assessment of the deviations between the experimental and predicted retention values provides insight into the mechanism of interaction between peptide solutes and the non-polar stationary phase. Clearly, in the case of large polypeptide solutes where highly stabilised secondary or tertiary structures may exist, the interactive properties of the solute will not be predicted from the summated coefficients based solely on the linear amino acid sequence. Furthermore, the use of retention coefficients only addresses the thermodynamics of the separation process and it is impossible to assess properly the degree to which the system can be optimised in terms of maximising peak capacity without prior access to experimental bandwidth and retention data, i.e. knowledge of the kinetics of the retention process. Overall, it can be concluded from several studies that the theoretical treatment based on LSS concepts used to derive log k versus (p relationships provides a useful approximation to the observed results of gradient elution. However, for such non-mechanistic models to have wide utility, they should also adequately describe and differentiate different band-broadening phenomena. These aspects can be evaluated from comparison of relationshps between peak capacity (PC) and separation variables. Alternatively, experimental bandwidths can be compared with bandwidths calculated on the basis that zone dispersion for the peptide is described by the general plate height theory originally derived for low molecular weight solutes over a wide range of gradient conditions.

4. Bandwidth relationships of peptides in RP-HPLC Complex mixtures of polypeptides are now typically chromatographed on n-alkylsilica stationary phases under gradient elution conditions. This practical requirement arises from the pronounced dependency of the relative retention, i.e. S and D parameters, and the bandwidth a, of polypeptides and proteins on the volume fraction, +, of the organic solvent modifier. Because of the small diffusion coefficients of polypeptides and proteins in water-organic solvent mobile phases, the expected theoretical plate numbers, N , should be significantly smaller than the N values obtained with low molecular weight organic molecules separated under equivalent reversed phase conditions. However, other effects, mediated by the silanophilic properties of the heterogeneous N-alkyl-modified stationary phase surface, by specific solvation or buffer interaction equilibria, and by conformational phenomena, also contribute to the bandwidth dependencies of these polyionic

127

solutes on experimental conditions. Although it is frequently assumed that all the solute components in a complex mixture can in principle be eluted with well-designed gradient systems from a given column with the same relative bandwidth, careful examination of actual chromatograms for polypeptides separated under the same gradient conditions of t,, F and A@ usually reveal that this requirement is rarely achieved in practice. Furthermore, when gradient or column conditions are changed experimentally, the bandwidths of peptide components in a mixture may not immediately appear to be correlated in a manner expected for the change in experimental parameters. Regardless of the physicochemical origin of this anomalous bandwidth behaviour of peptides and proteins it is now clearly apparent that the current theoretical approaches which describe the thermodynamic and kinetic processes of macromolecular solute migration in interactive HPLC systems do not yet quantitatively address the implications of a single solute with multiple interacting sites or varying diffusional properties and molecular shape as a consequence of time dependent exposure to a particular chromatographic environment. For example, the derivation [48,49] of the theoretical equation for the chromatographic bandwidth a,, namely a,=

+

[ t , F ( l + l/%)]/(ln 10)NO.’SA+= [ ( k / 2 ) 1]GtoFN-O.’

(19)

is based on the assumption that the surface area of a peptidic solute of a defined molecular weight can be characterised in terms of a constant hydrodynamic shape throughout the chromatographic separation. Under these conditions, it would be anticipated that the normalised ratio of the experimentally observed bandwidths to the calculated bandwidths should approach unity over the normal operational range of k values. However, in cases where chromatographic residence time effects result in changes in peptide secondary structure or where other secondary equilibrium effects operate, the experimental bandwidths have been found to significantly exceed the values predicted on the basis that the solute behaves as a conformationally rigid species which interacts with a single class of binding sites during its passage along the column. This is particularly evident in Fig. 9 which shows plots [4] of uv,exp/uv,cdc versus l / b for a series of six peptides related to and including human /?-endorphin (peptide 6) which, as discussed below, has the capacity to form an amphipathic helix at the C-terminus, when in contact with hydrophobic surfaces. Band-broadening relationships can be further analysed through the comparison of experimental and calculated peak capacity data. The peak capacity for a chromatographic separation of gradient time tG and average resolution equal to unity for all peptide pairs is given by

Pc =~ G F / ~ U ,

(20)

where a, is the experimental bandwidth measured in volume units (one standard deviation). Substitution of equation (19) into equation (20) results in the expression

128

Fig. 9. Plot of uvv.exp/uv,cdc versus l / b for the P-endorphin-relatedpolypeptides 1-6 (Table.2). Data acquired under conditions of different gradient time tG = 20, 30, 40,60 and 120 min, with the same mobile phase composition limits (water containing 0.1%TFA to water-acetonitrile (50 :50) containing 0.1%TFA) at a constant flow rate of 1 ml/min. Column, developmental C,,, d, = 6 pm, pd = 15 nm, 25 cmx4.6 mm ID. The value of uv.cdcwas calculated from (a) uv,cdc = [ t , F ( l + l/L)]/(ln 10)N0.5SA@ and (b) uvv,cdc = [(k/2)+ 1]GtoFN-0-5(equation 19). From [49].

where 0, is the solute diffusion coefficient in the mobile phase and C is the Knox equation parameter which accounts for resistance to mass transfer at the stationary phase surface. It is therefore possible to further optimise a chromatographic separation by maximising the peak capacity through manipulation of experimental conditions by changes in mobile phase or column configuration. Equation (21) also for separations carried out predicts a linear relationship between PC and k0.25/C0.5 under regular reversed phase conditions, and where conformational reorientation is extremely rapid compared to the chromatographic residence time of the solute. However, several examples [9,10,14,49]have been reported where the experimentally observed peak capacity, PCexp, was significantly lower than PCcalcdetermined according to equation (21) and where at long gradient times, plots of PC versus k 0.25/C0.5 deviated from linearity. For example, the analysis of the experimental0 bandwidth behaviour of a series of peptide analogues related to a segment of myosin light chain which is illustrated in Fig. 10 revealed significant discrepancies between experimental and theoretical peak capacity data even though the peptides had identical compositions and molecular weights. Thus small differences in the N-terminal sequence of these peptides imparted a range of kinetic and/or diffusional properties so that the precise values of for example, Om,for these solutes could not be predicted on the basis of molecular weight alone. Clearly, more complex structural features must be accommodated into band-spreading model development in order to describe more accurately the RP-HPLC behaviour of

129

a

300

b

250

t

6 9.10

150

100

50

I

0

2

4

6

-

0

2

4

6

k O'*' / c O ' I

Fig. 10. Plots of peak capacity (PC) versus k0.25/C0.5 for the myosin-related peptides 1-10 (Table 2). The data correspond to values obtained from varied tG experiments ( t G = 20, 30, 40,60 and 120 min) and flow =1 ml/min. The PC value in panel (a) was determined from the expression PC = [ l . 1 5 A ~ ( t o ~ , ) 0 ~ 5 k 0 ~ 2 5 ] / 2 d(equation ~ C o ~ 5 21), while the PC value in panel (b) was calculated from the equation PC = tG/4,,,exp(equation 20). See legend to Fig. 5 for the chromatographic details. From [lo].

peptide solutes. The explanation for the differences in the peak capacity behaviour for peptide samples must reside in the nature of the intimate association between solute solvation and solute conformation in the extraparticulate and intraparticulate spaces of the stationary phase surface. The development of a quantitative model which describes all aspects of the influence of polymodal porous structure per se on the thermodynamic and kinetic properties of peptide migration is now possible due to the recent development of improved analytical tools including the development of non-porous stationary phases [16] with particle diameters between 0.75 and 2.1 pm. However, while anomalous bandwidth behaviour may be in part due to the complex kinetics associated with the migration of biopolymer solutes through the polydisperse porous structure of reversed phase packings, it is the molecular composition of the interactive segment of the solute which presents itself to the chromatographic surface that ultimately determines the thermodynamic properties of the solute.

130

’

I p-EP

t

V-EP a-EP

1 - 1 o.6

t

0.4

0.2

0 YGGFMT SE K S OTPL V T L

1

10

F KNA I

20

I KN AY K K G E

30

Residue Fig. 11. Helix probability profile for human /3-endorphin (peptide 6 , Table 2) in water ( 0 ) and in the presence of anionic lipids (0).Note that in the absence of lipids there is no potential for the formation of a C-terminal a-helix. Furthermore, the low probability of a-helix formation for a- and y-endorphin may also be correlated with the range of affinities which these peptides exhibit for different opiate receptors.

Furthermore, it is the number of interactive species derived from a single solute, and the corresponding range of thermodynamic and kinetic properties of those migrating species which will be responsible for the experimentally observed bandwidth behaviour. The estimation of which part of a polypeptide is involved in the binding to the stationary phase surface under a defined set of conditional parameters would provide some insight and predictive power into the chromatographic behaviour of a particular polypeptide. While a battery of peptide secondary and tertiary structure determinations is required, considerable information can be obtained from the determination of hydropathy profiles [14,501 based on the amino acid sequence. The resulting data can be used to assess the probability that a particular segment of a polypeptide will interact with a particular type of ligand such as hydrophobic surfaces. Discrepancies between retention properties and either summated hydrophobicity or linear hydropathy parameters are expected to become more significant as the molecular size of the solute increases. A number of algorithms are available to predict the secondary structure of peptides and proteins such as the Chou-Fasman [51] method for predicting a-helix and P-sheet formation and other procedures [52,53] which determine the probability of helix formation in a particular solvent environment. These approaches assist in the location of potential hydrophobic areas on the surface of a molecule via characterisation of amphipathic regions. For example, the probability profile shown in Fig. 11 indicates that an amphipathic a-helix can form in the C-terminal region of human P-endorphin, a peptide which

131

Lys

21

31 Ghl

Fig. 12. Representation of the carhoxyl terminal (residues 14-31) moiety of human fl-endorphin(peptide 6, Table 2) on an Edmundson helical wheel [54]. If P-endorphin chromatographed at any time with a carboxyl terminal amphipathic a-helical structure, the segments incorporating (Leu-l4)-(Phe-l8)-(Ala21)-(Asn-15) and (Val-15)-(Ile-22)-(Ala-26) would represent the sites most likely to interact with a reversed phase support.

exhibits bandwidth behaviour consistent with the formation of stabilised secondary structures [14]. The three-dimensional structure of the helix can be represented by two-dimensional projections or helical wheels [54]. Such a wheel is shown in Fig. 12 for the carboxy-terminal regions of human /3-endorphin, where the potential hydrophobic segments which could result in chromatographic behaviour that is significantly different from the random coil structure is clearly apparent. However, since the peptide helical structure cannot be directly monitored in chromatographic systems by conventional techniques such as circular dichroism, alternative spectroscopic methods are required. Recent studies [55,56] on the conformation of proteins adsorbed onto various n-alkylsilicas in the presence of aquo-organic solvents using fluorescence and Fourier transform infrared procedures, have clearly demonstrated the existence of surface-associated protein conformational changes induced by the hydrocarbonaceous ligand or by organic solvents. However, while the more advanced fluorescence and multiwavelength detectors can detect gross changes in protein conformation in chromatographic systems [57,59], accurate quantitation of the more subtle effects of small shifts in conformational equilibria which may be induced by interaction with non-polar surfaces requires more sophsticated approaches to the analysis of chromatographic data. Recent studies [23,60,61] on the characterisation of conformational equilibria for biopolymers at liquid/ solid interfaces have provided a theoretical framework for the treatment of multizoning chromatographic phenomena, and represent the most recent developments in the understanding of the mechanism of peptide and protein separations.

5. Dynamic models for interconverting systems For a given protein the intrinsic capacity factor, k', is determined by the overall equilibrium constant, K,, for its distribution between the stationary phase and the

132

mobile phase. In RP-HPLC as well as in other interactive chromatographic modes, it is often assumed that the chromatographic retention time is very much greater than the half-life of protein unfolding, protein re-orientation at the stationary phase surface, protein-buffer ion interaction or protein-solvation phenomena. When such conditions apply and no detectable change in the normalised concentration profile occurs throughout the duration of the experimental observations, then the system is considered to be at apparent equilibrium and is ascribed as ideal or regular in its chromatographic behaviour. However, it is well known that the mass distribution coefficient of the observed chromatographic capacity factor is a time-averaged function of the different forms of the solute as it traverses the column. Secondary phenomena often impinge upon the dominant chromatographic distribution process established between the solute and the two phases. As has been previously discussed in detail, some of these effects can be advantageously employed to enhance selectivity in a predictable way. However, secondary processes such as conformational interconversion, protein-protein aggregation, multimer-monomer dissociation, metastable adsorption or sol-gel thermal transitions can also occur with polypeptides and proteins in chromatographc systems with generally undesirable consequences.

1

120MINS

ELUTION PROFILE

Fig. 13. Representative elution profile of soyabean trypsin inhibitor undergoing dynamic interconversion during chromatographic separation on a 30X0.4 cm column packed with 10 pm, n-propylphenylsilica, flow 2 ml/min, linear gradients of 20 and 120 min from 15 mM orthophosphoric acid to acetonitrile-15 mM orthophosphoric acid-water (1:1, v/v). Reinjection of component A or component B demonstrated a time-dependent conversion to component C. Reinjection of component C resulted in the emergence of a single peak with the same elution time and peak shape.

133

The participation of all these different secondary phenomena will affect the apparent capacity factor, given by the sum of the capacity factors for each form weighted by its mole fraction, as well as the peak variance, u,?, when the kinetics of the various processes involved are not rapid compared to the time scale of the chromatographic separation. In such circumstances the appearance of asymmetrical or multiple peaks for an apparently homogeneous solute such as the chromatographic profile shown in Fig. 13 for soybean trypsin inhibitor where both native (folded) and inactive (unfolded) forms are evident, will be very dependent on the nature of the solute mixture as well as the choice of the chromatographic conditions. Furthermore, in contrast to the separation of the small molecules, it is quite likely that anomalous peak profiles will more readily occur when random or empirical selection of chromatographic conditions is made. The ability to detect and resolve intermediate states of a multistep conformational transition will depend on the sensitivity of the measurement, the relaxation times associated with the different phenomena, the magnitude of the differences in retention times for the different species and the peak variance of each species. There have been two main approaches to incorporate these features into models which describe the dynamic effects of secondary equilibria in chromatographic separation. More than 25 years ago, Keller and Giddings [62] derived a stochastic probability model to account for multiple zones due to interconverting species in paper chromatography and other forms of polar chromatography. This model appears equally pertinent today for evaluating multiple peaks associated with conformational equilibria or other secondary equilibria in the RP-HPLC of polypeptides and proteins. If a protein undergoes a two-stage interconversion in both the mobile phase and at the stationary phase surface then a retention cycle which represents the process of distribution of the protein in its native form Pm,o and two unfolded forms Pm,land Pm,2 between the two chromatographc phases can be written as shown below: Mobile Phase

IC32

k63

Stationary Phase Such a retention pathway may occur in the RP-HPLC of papain or soyabean trypsin inhibitor. If the rate-determining step for the pathway is associated with the conformational unfolding Pm,l+ Pm,2then the distribution can be approximated by a four-component cycle. Thus, if the fraction of time the protein, P, spends in one form is represented by t , then the probability that this fraction is in the range t + d t is given by Pi(t)where i = 1, 2, 3 . . . , representing each of the forms. If the

134

interconversion cycle is represented by only four forms, the probability that P starts as P,,,o and after one cycle ends as Pm,ocan be given by P : , ( t ) d t = [rlr2(l-t)/t]

exp[-rl(1-t)-r2t]Z[4rlr2t(l-t)]1/2t

(22)

where rl = ( @ k 1 2 k 2 3

+ k14k21)t*/k21

(23)

and

where t *

= separation

time and

At separation time t * = 0, a mixture of Pm,oand P,,,l in apparent equilibrium will be introduced at the column inlet. When the overall rate constants for the forward and reverse processes of interconversion, r,/t * and r2/t *, are of the same order of magnitude as the rate constants for adsorption and desorption from the stationary phase, the processes represented by Pm,o+ Ps,o and Ps,l assume greater significance in the overall probability distribution. Under conditions of high mass recovery and relatively rapid adsorption-desorption kinetics, the overall concentration profile can be obtained from the summated probability distributions which in each case are properly weighted by the fractions a and b of molecules of P in the initial Pm,o and P,,, forms injected onto the column at t * = 0, such that

*

P( t ) = a [ Pi( t ) + Pp( t )]

+ b [ P:(

t)

+ P4"(t )]

(24)

P( t = 0 ) = a exp( - rl)

(27)

P ( t = 1) = b exp( - r2)

(28)

By assuming Gaussian distributions for the concentration profiles of Pm,oand P,,,l centred around t = 0 and t = 1, respectively, and by allowing a single diffusion coefficient to describe the combined effects of the chromatographic process for each conformational form, then both P ( t = 0) and P ( t = 1) can be made discrete functions and the probability distributions of the interconverting species, separated by retention time differences of Atql and Atq2 can be computed. The calculated concentration profile for bovine trypsin undergoing a two-stage dynamic interconversion during RP-HPLC is shown in Fig. 14. This can be compared to Fig. 15 which illustrates the influence of competing equilibria on the experimentally-observed multizoning behaviour of trypsin under different experimental conditions

135

2.0

-

13

-

A

Y C

0

0

14

t Fig. 14. The calculated concentration profile for bovine trypsin undergoing dynamic interconversion whilst chromatographed on a reversed phase column. It is assumed that the interconversion processes occur by a two-state reversible transition with overall forward conversion and reverse conversion rates r , / f * = r 2 / t * = 1.25 X 10K3 sec-' and that at t * = 0 and equilibrium mixture of two interconverting components of equivalent mole fractions is initially loaded onto the column. It is further assumed that the migrating zone for each component generates a Gaussian distribution profile with u = 0.1 and that the effective diffusion coefficients of both forms are the same. From [23].

15 MlNS

I

e

r

N

0

0

ELUTION PROFILE

Fig. 15. Changes in bandshape of bovine trypsin chromatographed on a 13 nm pore diameter octadecylsilica stationary phase as a function of flow rate and residence time at the stationary phase surface. A linear gradient from 0.1% TFA-water to 0.1% TFA-water acetonitrile (l:l, v/v) was used in all experiments. The bandwidth of the trypsin sample in the 15 min, 0.5 ml/min experiment was equivalent to 4,v=1050 pl. BAEE assays of the recovered zones revealed that the trypsin-like activity of all zones was also similar. From [23].

136

which correspond to variation in separation time and chromatographic dwell. Equivalent expressions can be derived for cooperative and non-cooperative transitions involving multistep conformational perturbations with several intermediate states, or non-Gaussian concentration profiles due to heterogeneous interactions of the stationary phase surface. A major criticism of the stochastic probability approach is that relatively slow secondary reactions, for which the ‘near-equilibrium’ assumption does not apply, cannot be accommodated. In this situation, it is necessary to derive and solve simultaneous partial differential equations for mass conservation and obtain expressions for the first and second moments of the elution profile and the concomitant plate height arising from slow kinetics of secondary equilibrium. If, once again, the process can be represented as involving the reversible binding of two forms, the resolution of the interconverting species can be given by [59]

where

where @ is the phase ratio (K/Vm), ki, are the respective rate constants for adsorption, desorption, unfolding or refolding, ui is the peak width of component i, L is the column length and uo is the linear velocity. The plate height increment due to slow kinetics of interconversion, H,,, can be determined by

where

and k o and k , are the capacity factors for the two interconverting forms. The Damkohler number represents the ratio of the time taken by the protein to passage along the column in the mobile phase to the overall relaxation time for all conformation interconversions in the chromatographic system. The influence of the Damkohler number on the chromatographic profile is shown in Fig. 16. When this ratio is small, and in the limit approaches zero, then the chromatogram for a four-component cycle will reflect the average macroscopic behaviour of a fully unfolded form or alternatively two peaks separated by a time interval trn(kl,/k2,k43/k34). Conversely, when 0,is very large, kinetic effects associated with conformational interconversion essentially vanish. However, at intermediate reaction rates

137

Time

Fig. 16. Computer simulation of the influence of the magnitude of the DamkoNer number on the elution profile of a peptide undergoing a 4-cycle interconversion. Such behaviour has been observed in our laboratory for the dipeptides L-leucyl-L-proline, L-valyl-L-proline and L-alanyl-L-proline.

where 1 < 0,< 10, complex elution profiles which are dependent on the equilibrium distribution of the two species, the rate of interconversion, the chromatographic conditions and the intrinsic column efficiency, will be obtained. The influence of the Damkohler number on the dependence of the bandwidth on the capacity factor is shown in Fig. 17. Relatively slow kinetics of interconversion which is characterised by a small Damkohler number causes the overall bandwidth to go through a maximum at intermediate retention times, and significantly high H,, can be obtained at relatively small k’ values. Detailed experimental data on the rate constants associated adsorption/ desorption kinetics or conformational interconversion of different forms of a protein chromatographed on n-alkylsilicas are currently very sparse. The kinetics of denaturation of several proteins on n-butyl-bonded silica surfaces have been reported. Fig. 18 for example, shows the dependence of peak area on the incubation time of lysozyme on the bonded phase surface, from which rate constants for interconversion on the stationary phase, i.e. k,, were derived [63]. The graphical representations derived from quantitative numerical solutions of the probability distributions

k’

Fig. 17. Plots of bandwidth versus capacity factor k’ for different values of the Damkohler number, 0,. The bandwidth u was calculated using equations (30-32).

138

5.0

a

-

4.5

0

40

3.5 0

5

10

15

20

25

Incubation Time (min)

Fig. 18. First-order kinetic plots of the rate of denaturation of lysozyme at various column temperatures as a function of incubation time on the bonded phase surface. Log A = logarithmic area of the active peak. Incubation solvent, 10 mM H3P04 (pH 2.2). Column, LiChrospher SE-500 C4, d,=10 pm. Solvent A = 10 mM H,P04 (pH 2.2); solvent B, 1-propanol-water (45 :55, v/v) in which the total H3P0, concentration is 10 mM. Gradient rate = 3% propanol/min, 15 min, flow = 1 ml/min. From [63].

I

F- O.Sml/min

F - 1.5 ml/min

I

Da= 5

Time

Fig. 19. Experimental and simulated elution profiles of L-alanyl-L-proline. The experiments were carried out at 22OC, pH 7.07, using 50 mM phosphate buffer as the mobile phase and 5 p m Partisil ODS (25 cm x 4.6 mm ID) as the stationary phase. From [61].

139

or the mass-balance equations with various combinations of selected values for the rate constants, equilibrium constants and relative retention differences can be used to simulate elution profiles and where feasible to provide visual comparison with experimentally observed chromatograms. An example of t h s approach is shown in Fig. 19 for the chromatographic analysis of L-alanyl-L-proline, whereby 0,values have been manipulated to simulate experimental profiles. The application of these analytical expressions allows the band-spreading changes due to slow lunetics of secondary equilibria to be used to determine rate constants for the folding-unfolding transitions in both the mobile phase and stationary phase. The development of a data base of the various kinetic parameters involved in the interaction between proteins and stationary phase systems will provide the fundamental insight needed to accommodate the various mechanisms of surface induced denaturation of peptides and proteins.

6. Conclusion Highly purified peptide and protein samples can only be achieved through the application of several high resolution separation techniques of which RP-HPLC represents one possible dimension. Compared to some of the other adsorption modes of chromatography the current understanding of the mechanistic basis of reversed phase chromatography of peptides and proteins is more developed due to the advances in stationary phase preparations and the speed with whch data could be accumulated and analysed. As a consequence, several models can now be described which provide the first steps towards quantitative descriptions of peptide retention behaviour in terms of structure-retention relationships. Ultimately, detailed analyses of relative retention, band-shape and on-line spectroscopic properties will provide a complete definition of the functional status of a particular chromatographic peak. These advances will collectively permit further characterisation of the experimental factors which influence the three-dimensional structure of polypeptides and proteins in chromatographic systems whether these systems are based on hydrophobic, coulombic or another type of adsorptive surface. In t h s context, RP-HPLC is at the forefront of developments in new concepts on structure-retention relationships - developments for which the descriptive title ‘chromatopography’ has been coined [59] - the emerging science which fuses chromatographic principles and techniques with surface topographical mapping of peptides, proteins and related biomacromolecules.

A cknowledgements The support of the Australian Research Grants Commission, the National Health and Medical Research Council of Australia, the Monash University Special Research Grants Committee, the Potter Foundation and the Buckland Foundation for sponsoring over the past decade various research projects summarised in part in this

140

chapter is gratefully acknowledged. M.I. Aguilar holds a Postdoctoral Research Fellowship of Monash University.

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142 84 85 86 87 88 89

Pekin, F., Presentini, R. and Antoni, G. (1987) J. Chromatogr. 97, 365. Heam, M.T.W., Guthridge, M. and Bertolini, J. (1987) J. Chromatogr. 397, 371. Leadbeater, L. and Ward, F.B. (1987) J. Chromatogr. 397, 435. Stone, K.L. and Williams, K.R. (1986) J. Chromatogr. 359, 203. Goheen, S.C. and Chow, T.W. (1986) J. Chromatogr. 359, 297. Kunitani, M., Hirtzer, P., Johnson, D., Halenbeck, R., Boosman, A. and Koths, K. (1986) J. Chromatogr. 359, 391. 90 Tempst, P., Woo, D.D.L., Teplow, D.B., Aebersold, R., Hood, L.E. and Kent, S.B.H. (1986) J. Chromatogr. 359, 403. 91 Pearson, S.D., Dixon, J.D., Nothwehr, S.F. and Kurosky, A. (1986) J. Chromatogr. 359, 413. 92 Nyberg, F., Peknow, C., Moberg, U. and Eriksson, R.B. (1986) J. Chromatogr. 359, 541. 93 Neame, P.J., Christner, J.E. and Baker, J.R. (1986) J. Biol. Chem. 261, 3519. 94 Heiring, H., Kirsch, D., Obermaier, B., Ermel, V.B. and Machicaw, F. (1986) J. Biol. Chem. 261, 3869. 95 Martin, J.L., Rose, K., Hughes, G.L. and Magistretti, P.J. (1986) J. Biol. Chem. 261, 5320. 96 Gibson, B.W., Poulter, L., Wilham, D.H. and Maggio, J.E. (1986) J. Biol. Chem. 261, 5341. 97 McKeehan, W.L., Sakagami, Y., Hoshi, H. and McKeehan, K.A. (1986) J. Biol. Chem. 261, 5378. 98 Vlasuk, G.P., Benan, G.H., Scarborugh, R.M., Tsai, P.K., Whang, J.L., Maack, T., Flarmargo, M.J., Kirscher, S.W. and Abraham, J.A. (1986) J. Biol. Chem. 261, 4789. 99 Skerwood, N.M., Sower, S.W., Marshak, D.R. Fraser, B.A. and Bronnstein, M.J. (1986) J. Biol. Chem. 261, 4812. 100 Decamp, D.L. and Colman, R.F. (1986) J. Biol. Chem. 261. 4499. 101 Gerard, C., Showell, H.J., Hoeprich, P.D., Hugli, J.E. and Stimler, N.P. (1985) J. Biol. Chem. 260, 2613. 102 Norman, J.A. and Chang, J.Y. (1985) J. Biol. Chem. 260, 2653. 103 Huynch, Q.K. and Snell, E.E. (1985) J. Biol. Chem. 260, 2798. 104 Sliwkowski, M.V. and Stradtman, T.C. (1985) J. Biol. Chem. 260, 3140. 105 Suzuki, T., Furukohri, T. and Gotoh, T. (1985) J. Biol. Chem. 260, 3228. 106 Hitchcock-Degregori, S.E., Gerhard, M.D. and Brown, W.E. (1985) J. Biol. Chem. 260, 3228. 107 Butkowski, R.J., Wieslander, J., Wisdom, B.J., Barr, J.K., Noelken, M.E. and Hudson, B.G. (1985) J. Biol. Chem. 260, 3739. 108 Weldon, S.L. and Taylor, S.S. (1985) J. Biol. Chem. 260, 4203. 109 Kennedy, B.P. and Davies, P.L. (1985) J. Biol. Chem. 260, 4338. 110 Mehansha, H., Clements, S., Sheares, B.T., Smith, S. and Carlsen, D.M. (1985) J. Biol. Chem. 260, 4418. 111 Pan, L.C., Williamson, M.K. and Price, P.A. (1985) J. Biol. Chem. 260, 13398. 112 Miziorko, H.M. and Behnhe, C.E. (1985) J. Biol. Chem. 260, 13573.

L.L.M.Van Deenen (Fkis.) Modern Physical Methods in Biochemistry, Part B 1988 Elsevier Science Publishers B.V. (Biomedical Division)

A. Neuberger and Q

143

CHAPTER 6

X-ray and neutron solution scattering STEPHEN J. PERKINS Kennedy Institute of Rheumatology, Bute Gardens, Hammersmith, London W6 7 0 W, UK

1. Introduction In application to structure determinations, modern physical techniques can be subdivided into three groups of resolution, namely those at high, sub-atomic resolution, those at atomic resolution, and those at low, overall resolution. At the sub-atomic level, techniques such as nuclear magnetic resonance [ 1-31 permit the microenvironment of single atoms within individual residues to be studied. At the atomic level, single crystal diffraction studies gives details of the molecular arrangement of the residues within the macromolecule, and for this reason, this is the most powerful structural technique available [5,6].Low resolution methods include not only X-ray and neutron solution scattering [7-311 but also other related techniques such as total sequence determinations, electron microscopy [32], light scattering [33,34] and hydrodynamic studies [35],all of which report on various aspects of the overall macromolecular shape. These complement powerfully the crystallographic method for a number of reasons, including those cases where the macromolecule cannot be crystallized or where it is required to work in a more physiological environment in solution. This review presents a survey of the use of both X-ray and neutron scattering methods in biologcal applications. The common-day occurrence of solution scattering occurs in the diffuse halo of light that surrounds a bright street lamp on a foggy evening. Through Rayleigh scattering, the lamplight is dispersed by the atmospheric water globules. X-ray and neutron scattering (and light scattering also) constitute different physical applications of the same diffraction event. The different properties of these radiations can be exploited as required. Solution scattering is also known as diffuse scattering, and also as small-angle and wide-angle scattering. Solution scattering investigates the overall shapes of macromolecules that are in solution and randomly orientated, and out to a structural resolution of up to about 1 nm. Since diffraction is involved, the theory originates from Bragg’s Law of Diffraction. Since the macromolecules are not orientated, as they are in crystals and fibres, unique structures cannot be * Presenf address: Department of Biochemistry and Chemistry, Royal Free Hospital School of Medicine, Rowland Hill Street, London NW3 2PF, UK.

144

determined by solution scattering. This would be tantamount to saying that a three-dimensional structure can be derived from a one-dimensional scattering function. In fact, solution scattering leads to the determination of several model-independent molecular parameters, most notably the radius of gyration R, and the niolecular weight M,. With additional curve analyses, solution scattering is at its most effective in rejecting unsatisfactory shape models. Such models would have originated in the course of testing a range of plausible models within the analyses, or have been obtained from the use of other physical techniques, most notably electron microscopy. The use of as many constraints as available, such as the knowledge of the complete sequence, will reduce the range of allowed shape models. In several instances, this leaves one or two structural unknowns which can then be determined by solution scattering. Biophysicists can then proceed to elucidate the relevance of the solution structure to the known function of the macromolecules in terms of biological organizations, interactions and recognition. The chapter is subdivided into two parts. Part A deals with the theoretical and practical aspects of solution scattering work, whle Part B deals with the biochemical applications of the method to proteins, carbohydrates, lipids and nucleic acids.

Part A: Theoretical and Practical Aspects

2. Theory of X-ray and neutron scattering The two major themes in scattering theory are the scattering properties of biological materials and the geometrical relationships between these materials within the macromolecule. These are embodied in the Debye equation. The most comprehensive account of X-ray scattering theory is given in Glatter and Kratky’s compendium [7]. 2.1. Scattering phenomena and their angular ranges

2.1. I . X-ray scattering Scattering occurs wherever electromagnetic radiation interacts with matter. X-rays are scattered by electrons [4]. There are two components of scattering by X-rays, i.e. Thomson or coherent scattering, and Compton or incoherent scattering. The alternating electric-field vector of the incident radiation imparts an alternating acceleration to the electron, whereupon the electron itself becomes an oscillating charge which itself emits electromagnetic waves of the same wavelength h but phaseshifted by n. This scattering occurs in all directions, but remains in the same phase.

145

This is coherent scattering which will lead to interference phenomena and solution scattering. Thomson’s equation gives the intensity of scattering by one electron: e4 L=At=(,.P)(

1-cos22e 2

)($)

The first bracketted term is 7.90 fm2 (Thomson’s constant), where e and m are the charge and the mass of the electron and c is the speed of light. Thus the scattering by one electron is reduced by over compared to the primary beam intensity P (and that by a proton will be over l o 6 times smaller still for reason of the proton mass). The second bracketted term is the polarization factor, whch in solution scattering is unity since 28 is restricted to small values (see below). SD is the sample-detector distance. Note that the scattering length of one electron f is the square root of Thomson’s constant, or 2.81 fm (Table 1). The Compton scattering of X-rays is incoherent with respect to the incident beam and is best described as the elastic collision of an X-ray proton with an electron where both energy and momentum are conserved. This means that the X-ray wavelength is increased. In effect, X-rays are considered as particles and not as waves. Compton scattering increases with the angle 28, but is always small compared with that of Thomson scattering.

2.1.2. Neutron scattering Neutrons are scattered by nuclei, either by nuclear interactions with the atomic nucleus or magnetically if the nucleus has a magnetic moment [36]. Since nuclei are very small compared with the neutron wavelength, nuclei are in effect point scatterers, and there is no angular dependence of the scattering of neutrons. It is difficult to predict the calculated scattering from a given atom, since this depends on the nuclear mass, spin and energy levels and on the nuclear isotopes that are present. Nuclei with spin have two scattering factors, one for the spin-up state and one for the spin-down state. T h s leads to two types of neutron scattering, coherent and incoherent. Coherent elastic scattering results from the spatial distribution of nuclei within the particle, whch leads to interference phenomena and solution scattering. A plane wave of neutrons of wavelength X can be described by the wave function: ‘k(x )

= exp( i k x )

where k = 27~r/X.The scattered wave is usually written as:

where b is the scattering length of the nucleus and measures the probability of the scattering event. It is defined through the scattering cross-section u: (I=

outgoing current of scattered neutrons incident neutron flux

= 4nb2

146

TABLE 1 Scattering lengths for biologically relevant nuclei. Note that by the S.I. set of units, 1 fm the units of cm that are common in the early literature become 10 fm Nucleus Hydrogen Carbon Nitrogen Oxygen Sodium Magnesium Phosphorus Sulphur Chlorine

'H 2H C l4 N 0 23Na 24Mg 31 P 32s 35.37~1 35

c1

37c1

Potassium Calcium Iron

39K Ca 54,56,57~~

Fe 56Fe 57Fe 79,81Br 54

Bromine

Atomic number

f(20

1 1 6 7 8 11 12 15 16 17 17 17 19 20 26 26 26 26 35

2.81 2.81 16.9 19.7 22.5 30.9 33.7 42.3 45 .O 47.8 47.8 47.8 53.4 56.2 73.1 73.1 73.1 73.1 98.4

=

O o ) (fm)

=

m, so

b (fm)

- 3.742 6.671 6.651 9.40 5.804 3.62 5.3 5.1 2.847 9.580 11.8 2.6 3.70 4.64 9.51 4.2 10.1 2.3 6.79

X-ray and neutron scattering lengths are compared in Table 1, where f (X-rays) is seen to increase in proportion to the atomic number while b (neutrons) remains roughly at the same magnitude and is uncorrelated with atomic number. It is also seen that the probability of scattering of neutrons by a nucleus is reduced by over times compared with the incident flux. This is comparable to the case with X-rays above. Finally, Table 1 shows that the 'H nucleus has a large negative neutron scattering length. This implies that there is no phase shift of T relative to the incident wave when neutrons are scattered by 'H nuclei. This negative b for 'H is of crucial importance for neutron scattering in biology, and has major applications in contrast variation and label triangulation methods (Section 4). Incoherent elastic neutron scattering exists only for nuclei with spin (i.e. not for zero-spin nuclei such as '*C or l6O), and results from the interaction of random nuclear spin orientations with the spin of the incident neutrons. It is spatially isotropic. It is usually negligible, except again in the case of 'H nuclei where it becomes very large. This is most useful since it constitutes the basis of neutron scattering curve normalization on an absolute scale through the use of a H,O reference sample (Section 2.5). 2.1.3. Scattering angles, vectors and resolution The spatial arrangements of electrons or nuclei within the particle leads to diffraction phenomena which can be considered using Bragg's Law: X = 2 d sin6

147

where A is the wavelength, d is the diffraction spacing, and 28 is the angle of diffraction. The distances of relevance here occur in ranges of 1- 100 nm (units in this review are given in nm and not A or cm to correspond to the trend towards S.I. units). Thus for most X-ray scattering where A = 0.15 nm, 28 ranges inversely from 4.3" to 0.04". For neutron scattering where A = 1 nm, 28 ranges from 30" to 0.3". In light scattering, A can be 400 nm, whereupon the entire angular range from 0 " to 180" is filled. In X-ray scattering, sin 28 is often approximated to 28, hence the terms "small angle" and "solution" X-ray scattering are synonymous, while this is not necessarily true for neutron scattering. The resolution of a diffraction experiment is given by 27r/Qma, where Q,,, is the largest scattering vector used in data collection ( Q = 477 sin 8/A, where 28 is the scattering angle). At best, this is about 1 nm. Sometimes the resolution is defined as 2m/Qwhere Qminis the smallest Q that has been measured. This alternative definition corresponds to the largest dimension of the particle that can be measured by solution scattering. It should also be noted that various nomenclatures are in use for scattering vectors and angles. Thus Q has been represented alternatively by h , K , p. or q in the literature. Its usage is convenient for algebraic reasons, and is the most widely adopted convention in the field. In X-ray crystallography and some solution scattering work, Q is replaced by s as a represention of the reciprocal Bragg dimension (s = Q/27r = l/d). Some X-ray workers replace Q with the scattering angle 28 ( 2 8 = QA/27r, assuming sin 2 8 = 28). Care is needed to keep to one nomenclature and to define it. 2.2. The scattering event and the Debye equation The sum of all scattering events leads to the scattering curve, and can be analysed as follows [lo]. Consider two identical scatterers withm a macromolecule at 0 and P

/

lncidf radial

Fig. 1. Diffraction by two points 0 and P separated by a distance r within a single particle in a solution scattering experiment. A and B correspond to the perpendiculars to the incident and scattered beams. The unit vectors so and s define the incident and scattered radiation, and Q defines the scattering vector (s - so).

148

(Fig. 1).The unit vector defining the direction of the incident radiation is denoted as so, and the direction of the scattered radiation from an origin 0 is denoted by another unit vector s. Since scattering is elastic, the amplitude of so and s are equal, and are set as 2a/A. The scattering vector Q is given by (s - so), and Fig. 1 shows that its amplitude is 4a sin 8/A, where 28 is the scattering angle. The combination of scattering events from 0 and an arbitrary point P will lead to interference phenomena. When 28 is zero, the scattered waves are in phase and scattering is at a maximum, directly reflecting the sum of all scatterers. This is the basis of molecular weight determinations by X-ray and neutron scattering. When 28 is non-zero, the path difference between the waves scattered from 0 and P has to be considered. From Fig. 1, this is A 0 + OB, and this corresponds to a phase difference of 2a(AO OB)/A, since the oscillatory profile of a wave is given by sin(2~x/A) where x is the distance travelled by the wave. If the vector between 0 and P is r , then A 0 = rso and OB = -rs and the phase difference is r(so - s). This becomes simply rQ. The Debye equation which defines the intensity of the scattering curve Z(Q) as a function of Q can now be derived [6]. The amplitude of the scattered radiation in the direction of the vector s from P is given by:

+

A,

= Aefp

exp( - i r e )

where f, is the X-ray scattering factor at P (i.e. the total of electrons) and A , is the amplitude of scattering by one electron. For neutron scattering, fp and A , are replaced by bp and A,. The total amplitude of the radiation scattered by the particle over all points is then:

The scattering intensity I(Q) is the product of A(Q) with its complex conjugate A(Q)* and the algebra gives: I(Q) =A:C P

Cfpfq C O S ( ~ Q ) = I e F 2 ( Q ) 4

where F ( Q ) is the structure factor of the particle. To allow for the random orientation of macromolecules relative to the incident beam, I(Q) is now averaged. This requires the average of F 2 ( Q ) :

Since r takes all orientations equally, the average of cos(rQ) is needed also, and integration gives sin( rQ)/rQ. Thus the Debye equation is obtained:

149

Note that this expression depends only on the magnitude of Q and that scattering is symmetrical about the incident beam. The Debye equation is based on the following physical description of the sample. This is a monodisperse solution of identical particles, which are in random orientations relative to the incident primary beam, and act as independent entities (i.e. there are no interparticle spatial correlations). The above derivation has presumed also that the particles are in vacuo. If they are in solution, they are required to form a two-phase system of solute and solvent. In biology, this corresponds to dilute solutions of pure proteins or glycoproteins in a low-salt buffer. Complications arise in the case of polyionic macromolecules in low-salt buffers, such as nucleic acids. Here, interparticle correlation effects can readily occur and the macromolecule is surrounded by an ion-cloud of opposite charge (i.e. a three-phase system). Other complications can arise in the cases of polydisperse distributions of macromolecules, oligomerization or dissociation phenomena, and conformational changes. Different formulisms have to be derived for the analyses of these systems. 2.3. Scattering densities and allowance for solvent 2.3.1. Concept of scattering densities Since the scattering from biological macromolecules is observed in the solution state and not in vacuo, adaptation of the Debye equation is required. Since solution scattering works at the resolution level of 1 nm and more, scattering densities can be used to replace atomic scattering factors. Any dependence of the scattering density on scattering angles can be neglected. The X-ray or neutron scattering factor ( f p or b,) can be rewritten in terms of volume elements dup of scattering density p ( r p ) , where fp = p(rp)dvp= p(rp)d3rp.Thus the intensity of scattering is:

where the integration is taken over the macromolecular volume V. Consideration of the scattering density of the solvent ps and that of the macromolecule in vacuo p ( r ) leads to the contrast Ap, defined as the excess scattering density of the macromolecule in solution above that of the buffer; Ps

Hence

The above assumes that the macromolecule has a uniform scattering density p( r ) . In general, distinct regions of differing densities occur within biomolecular systems,

150 700 100 o/

Protein

,. 600 $

RNi

500

'9

0

T

400

x

g

c

300

u aJ

c

200

L

aJ +

;;

100

U

0

0 -100

r (cross section of protein-RNA sphere) (arbitrary units)

Fig. 2. Schematic variation of neutron scattering density for an object composed of a central sphere of RNA and a concentric outer shell of protein, i.e. a simple virus. The contrast difference Ap is the difference between the scattering density of the solvent ps and the solute pv. High positive and negative Ap are seen in 0 and 100% 'H20. The protein shell is matched-out in 43% 'H'O and the RNA core is matched-out in 72% *H,O. Note that for reason of solvent 'H-'H exchange, the average protein and RNA densities increase slightly on going'from 0 to 100%'H20. Solution scattering is observed where the solute and solvent densities are different. Note that the fluctuations in scattering densities p F ( r ) within each of the protein and RNA components do not disappear at their respective matchpoints. See Section 2.3 for a further explanation of the terms in Ap, ps, pv and pF(r).

and these are analysed by varying the contrast Ap. Conceptually, p ( r ) is divided into two parts (Fig. 2). These correspond to the mean scattering density p v and the fluctuation of scattering density p F ( r )about this mean. This leads to the definition of the contrast Ap as A p = p v - p s . Both pv and ps are calculated for the macromolecule and the solvent using composition data in terms of expressions in Cf/Vor D / V , where the total of scattering lengths is divided by the volume V. The fluctuation pF(r) is returned to below. Babinet's Theorem is applicable in contrast variation experiments, where "complementary objects produce the same diffraction effects". The scattering curve of a set of hollow cavities in a homogeneous medium will be identical with the scattering curve of the particles of the same shape as the hollow cavities but dispersed in vacuo. Situations resembling this can occur in neutron scattering (Fig. 2) if macromolecules of homogeneous scattering densities are viewed in high positive and high negative solute-solvent contrasts. 2.3.2. Scattering densities and volumes A compilation of the scattering properties of the major solvent systems and biological classes of macromolecules for this review is presented in Tables 2 to 6. Since detergents are useful in the solubilization of membranous systems, data for these are surveyed in Table 7. Summaries are presented in Table 2 and Fig. 3. Since

151 ELECTRON DENSITY (e. n m 3 )

300 400 500 Weight percentage sucrose 180C

n

0

:

50

RNA, DNI 1600

N

'p

1400

Carbohydrate Protein / Sucr ose

0 1200

[N E U T RONS

h

c Ln

; 1000

I

0

m

E

14

volume percentage *H,O I

I

I

I

/

I

2 0 40 60 80 100

Lipid

800

a, c c 0

g

600

a,

c

5

400

9

200

-> Ln

0

-

-

-

-

-

L

Lipid

7

6

200

400

600

860

1000 1200 1400

p s (Solvent scattering density in

10bnrri2)

Fig. 3. Summary of the scattering densities of biological macromolecules in neutron and X-ray scattering. In neutron scattering, the increase in density for each class as the 'H,O content increases is the result of 'H-'H exchange. Neutron contrast variation by H,O-*H,O mixtures is able to match-out each of the five classes shown, while X-ray contrast variation can only be performed in the range between the electron densities of lipids and proteins. From [23].

atomic weights, atomic numbers (electrons) and nuclear scattering lengths are well-determined quantities, the main uncertainty in the compilations of Tables 3 to 7 lies in the volumes used to calculate scattering densities. Volumes can be experimentally determined by various means, namely molar volume summations, crystallographic analyses of small molecules and macromolecules, densitometry of small molecules and macromolecules, and neutron matchpoint determinations [371. The complication arises through surface interactions with solvent water molecules. Comparison of these methods leads to slightly differing total volumes. Ths is due to hydration effects. The volume of a water molecule is determined by its hydrogen bonding arrangements and not by simple packing considerations. The apparent water volume can therefore change when water molecules bind in well-defined structural positions on a protein or nucleic acid surface. This water volume change will affect the apparent macromolecular volume. For example, the folding of a protein into its globular tertiary structure will exclude water molecules from the interior of the globular structure. Likewise, the formation of protein-protein or protein-nucleic acid complexes will involve the expulsion of water molecules from

152

the intermolecular interface. Polyanionic macromolecules such as nucleic acids or glycosaminoglycans,or strong zwitterions such as phospholipids can also be expected to perturb local solvent structures. In addition, the polyanionic species will bind cations that will also contribute a volume change. In conclusion, calculations of macromolecular volumes require a critical awareness of the methods employed. For solution scattering, solvent densities can be calculated from standard tables of buffer densities and compositions. This procedure will allow for the non-ideality of concentrated buffer solutions that are used in some X-ray scattering studies (Table 2). Macromolecular partial specific volumes V can be experimentally determined by densitometry, usually with a Paar digital density meter, to measure the density of the buffer Pbuff and the solutions psampover a concentration range: v=-(11 P buff

&

- Pbuff C

where the terms in p correspond to the mass density and c is the concentration, both in units of g/ml [38]. However, it is not necessarily true that densitometric V values can be directly employed in electron or nuclear scattering density calculations. Thus careful comparisons of V values are required with the volumes derived from X-ray or neutron matchpoint graphs from contrast variation experiments (Section 4.2.8). In general, for proteins and glycoproteins, densitometric volumes and electron densities are best calculated from the physical macromolecule volume from crystallographic data and allowing for the contribution of a shell of electrostricted water molecules (0.3 g H,O/g protein or glycoprotein). For neutron studies, neutron matchpoints for these systems are best predicted from composition data on the basis of the non-exchange of 10% of the main-chain NH protons (i.e. 5% of the total exchangeable content) and the crystallographic data on residue volumes [ 371; the hydration shell can now be neglected. For carbohydrates, lipids and nucleic acids, 'H-'H exchange at labile sites can be taken to be complete in these components. The data of Fig. 3 and Tables 2 to 7 are discussed in three further levels of increasing detail below: the contrast difference Ap (Section 2.3.3); the sensitivity of pv to the ratio of 'H:non-'H atoms or electron-rich atoms in neutron or X-ray scattering (Section 2.3.4); scattering density fluctuations p F (r ) (Section 2.3.5).

2.3.3. The contrast difference Ap Consideration of the contrast difference Ap in neutron and X-ray scattering in Fig. 3 shows that neutrons and X-rays are primarily distinguished by the range in which the solvent density ps can be varied. The neutron contrast variation method using 'H,O-*H,O mixtures easily encompasses the scattering densities of all four major macromolecular classes, i.e. lipids, proteins, carbohydrates and nucleic acids. In distinction, contrast variation in X-ray scattering is limited to the density range between lipids and proteins, and is therefore best applied to this type of system such as plasma lipoproteins. That 'H,0-2H,0 mixtures are able to span the neutron scattering densities of the four biological classes reflects the different 'H contents of

153

TABLE 2 Scatteringdensities of solvents and macromolecules.Note that by S.I. units 1 nm = units of 10" cm-2 become lo4 nm-2 X-rays nm-2) Buffers and solvents H2O

m, so the earlier

Neutrons (e.~m-~)

,H20 0.20 M NaCl in H,O 0.20 M NaCl in 2 H , 0 20%NaCl (w/w) in H,O (3.9 M) 20%NaCl in 2 H 2 0 (3.9 M) 20%NaBr (w/w) in H 2 0 (2.3 M) 50%Sucrose (w/w) in H,O (1.8 M) 50%Sucrose (w/w) in ,H,O (1.8 M) Ethanol Glycerol Deuterated glycerol

938 938 944 944 1050 1050 1060 1130 1130 754 1160 1160

334 334 336 336 373 373 377 402 402 268 412 412

Macromolecular classes Lipids Detergents Proteins Carbohydrates DNA RNA

870-960 840-1210 1150-1260 1380 1650 1670

310-340 300-430 410-450 490 590 600

nm-,) - 56.2

640.4 - 53.9 639.1 - 19.6 620.0 - 38.5 31.8 550.2 - 34.5 61.3 748.4

(at matchpoint) 0.1-0.4 - 0.1-1.0 2.2-2.6 2.7 4.0 4.5

(%,H,o) 0 100 0 100 5 97 3 13 87 3 17 116 10-14 6-23 40-45 47 65 72

each class. Thus lipids are rich in 'H atoms whle nucleic acids are depleted in 'H atoms. In the case of X-ray scattering, lipids possess large relative fractions of H and C atoms which are less electron-dense than H 2 0 molecules. Proteins, carbohydrates and nucleic acids possess fewer H atoms and greater numbers of N and 0 atoms, and this causes their electron densities to be greater than that of water. Figs. 2 and 3 show that three extremes of high solvent-solute contrasts are accessible to experiment, namely the two high positive A p encountered with X-ray and neutron scattering in H 2 0 solvents and the high negative A p associated with neutron scattering in H 2 0 solvents. All components of the macromolecular system make scattering contributions to the observed scattering curve. Figs. 2 and 3 show that the relative contributions of scattering densities are different in these three cases. In a protein-RNA complex, the scattering contribution of RNA is 270, 180, and 50% of that for the protein in that order for (1) A p with X-rays, (2) A p with neutrons in H,O, and (3) A p with neutrons in 2 H 2 0 . Thus while RNA dominates the scattering curve in protein-RNA systems studied by X-rays, it should be noted that neutron scattering can replicate this condition simply by working in buffers containing 25% 'H20. T h s shows the importance of the large A p range available by neutron scattering. Finally, it is also important to note that, when working in match-out conditions in 43 and 72% ' H 2 0 (Fig. 2), the experimental signal-noise ratios are much weakened compared with the high contrast regimes.

154

2.3.4. Mean macromolecular scattering densities p Solute scattering densities are now examined in more detail, starting with the average density pv. The data of Fig. 3 and Table 2 reveal relative differences in p v values among the four macromolecular classes. Thus neutrons can see a clear difference in the RNA and DNA scattering densities while this difference is much reduced in the case of X-rays. This reflects the replacement of a solvent exchangeable 'H atom in the RNA ribose with a nonexchangeable 'H atom in the DNA deoxyribose. However, that difference between proteins and carbohydrates is greater by X-rays than by neutrons. This forms the basis of X-ray contrast variation by the addition of sucrose to the buffer.

2.3.5. Scattering density fluctuations p (r ) Fluctuations in scattering densities pF( r ) are usually considered relative to the average scattering density p v within a given biological class, although they also correspond to the density difference between two different biological classes within a two-component macromolecule. These are important in contrast variation work. As schematically shown in Fig. 2, a residual scattering contribution from the protein component in 43% 2 H , 0 means that the scattering curve in that contrast will not result from only the RNA component. If p F ( r )is large at the matchpoint of one component in a two-component system, this reduces the utility of the densitymatching technique to obtain shape information on the other component. For proteins, Table 3 shows that hydrophilic amino acid residues have scattering densities that are larger by -.30 e . nmW3or 15% 2 H 2 0 than hydrophobic residues in X-ray or neutron scattering. Since soluble globular proteins possess hydrophilic surfaces and hydrophobic cores, such proteins have higher scattering densities at their surfaces than at their core. Table 3 shows that the (mean error) of the 20 neutron matchpoint values is 44.7 f 14.2%2 H 2 0 , i.e. a range of +32% among the 20 amino acid residues. If the bulk solvent electron density of 334 e . mP3 is taken as the starting point, the 20 electron density values are found to fluctuate likewise by 91 f 38 e . nm-3, i.e. a range of f42%.Neutrons and X-rays both therefore visualize proteins at comparable levels of density inhomogeneities and the effects of this will be larger at low contrast differences A p . In distinction, Table 4 shows that the common carbohydrate residues demonstrate reduced density variations, and these are similar at 5-12% for neutron data (46.3 f 2.5%2 H 2 0 , or f5%) and X-ray data (158 f 19 e .nm-3, or f12%). Discussions of p F ( r )values for nucleic acids, lipids and detergents are related to those for proteins and carbohydrates. The difference is that these fluctuations are pronounced within a given molecule, whereas for proteins and carbohydrates the fluctuations are best described in terms of separate hydrophilic and hydrophobic residues. Here, within each residue or molecule, hydrophilic polar groupings face outwards in contact with solvent, whle the hydrophobic bases or polyalkyl groups are buried within the structure away from the solvent. These are again characterised by distinct scattering densities. Nucleic acids can be usefully considered in terms of phosphate, carbohydrate and base moieties. Table 5 shows that these possess distinct scattering densities in X-ray and neutron scattering and have different

-

+

155 TABLE 3 Scattering properties of the twenty amino acid residues. The residues are arranged in order of increasing hydrophilicity from Ile to Arg. Electron and nuclear densities correspond to the volume of the unhydrated residues (see Section 4.2.8 and [37]). Neutron matchpoints are calculated on the assumption of full solvent 'H-'H exchange [37] Name

Atomic composition

Hydrophobic residues Ile I C,H,,NO Phe F C,H,NO Val VC,H,NO Leu L C6HllN0 =rp WC11HION2O Met MC,H,NO, Ala AC,H,NO Gly GCZH3NO iCys CC3H4NOS Tyr Y C,H,N02 Pro P C,H,NO

Exchange- Elec- Xb (fm) Volume Electron able trons ( X lo-, nm3) density protons (e.nn-,) (H2O) (,HZO) lographic) 1 1 1 1 2 1 1 1 1 2 0

62 78 54 62 98 70 38 30 53 86 52

13.948 41.385 14.781 13.948 60.345 17.628 16.447 17.280 23.036 47.189 22.265

24.361 51.798 25.194 24.361 81.171 28.041 26.860 27.693 33.449 68.015 22.265

168.8 203.4 141.7 167.9 237.6 170.8 91.5 66.4 105.6 203.6 129.3

367 383 381 369 412 410 415 452 502 422 402

Neutron matchpoint (% ,H,o)

21.9 40.2 25.8 21.9 50.9 25.1 40.5 58.6 45.9 48.5 32.8

mean 410f 39 37.5 k 12.8 Hydrophilic residues Thr T C4H,N02 S C,H,NO, Ser His * H C,H,N,O Glu E C,H6NO3 Asn N C4H6N,0, Gln Q C,H,N202 Asp DC,H,NO, LYS K C,H,,N,O Arg R C,H,,N,O

54 46 73 67 60 68 63 71 85

21.418 22.251 43.974 37.615 34.560 33.727 38.448 15.864 34.664

42.244 43.077 75.213 48.028 65.799 64.966 48.861 57.516 97.142

122.1 99.1 167.3 155.1 135.2 161.1 124.5 171.3 202.1

442 464 436 432

444 422 506 414 421

44.0 57.7 62.6 47.5 67.0 52.8 59.6 32.8 58.8

mean 442 k 28 53.6 f 10.6

* His is protonated.

-

relative magnitudes. The electron density of a free phosphate group ( 830 e . nm-3) is particularly high compared with the average electron density of ribose or deoxyribose residues ( - 470 e . nrnp3) and the bases ( - 580 e . nm-3). The neutron matchpoint of the phosphate group ( - 70% 2 H 2 0 ) is, however, intermediate between that of the ribose or deoxyribose residues ( - 35% 2 H 2 0 ) and the bases ( - 105%2H20).Thus the neutron cross-sectional properties of a simple double-helical nucleic acid structure observed at its matchpoint density of 70% 2 H 2 0 will be characterized by invisible phosphate groupings. Neutrons will visualize a higher scattering density at the centre of the helix than at the edges. Note that the density of ribose or deoxyribose residues are not readily distinguishable from those of amino acid residues (Table 3). The situation is reversed for X-rays, since the average

TABLE 4 Scattering properties of some common carbohydrate residues [37]. The electron densities correspond to unhydrated residue volumes Atomic composition Glc Gal Man Man (terminal) GlcNAc GalNAc Fuc (terminal) NeuNAc (terminal)

Exchangeable protons

C6H1005 C6H1005 C6H1005 6‘

Hl5’1

C8H13N05 C8H13N05 c6 H10°4

CI 1Hl.5NO8

Electrons

Hb (fm)

86 86 86 87 108 108 78 153

31.506 31.506 31.506 27.764 42.982 42.982 25.702 69.121

Volume ( x 1 0 - nm3) ~

62.745 62.745 62.745 69.416 74.221 74.221 56.941 121.186

171.9 166.8 170.8 170.8 222.0 232.9 160.8 326.3

Electron density ( e .nm - 3 ) 500 516 504 509 486 464 485 469

mean 492 + 19

Matchpoint (W 2 H 2 0 ) 46.5 48.1 46.9 48.3 44.9 42.8 43.0 49.9

Glycosarninoglycans

G k A . GIcNAc (hyaluronate) Gal.GlcNAc.SO, (keratan sulphate) GlcA .GalNAc.S04 (chondroitin sulphate)

C,,H*oNO,,Na

5

210

95.138

147.203

390.7

537

53.2

Cl,H,2NO13SNa

5

244

102.109

154.174

473.5

515

46.3

260

122.759

164.411

443.5

586

55.3

C14H1S”014SNa2

*

46.3 2.5

TABLE 5 Scattering properties of nucleic acid residues. The electron densities correspond to unhydrated residue volumes. Residue volumes were calculated using i j = 0.66 ml/g for ribose and the summations of molar atomic volumes for the bases as given below, and using V = 0.52 ml/g for RNA, whereupon the phosphate volume was best determined from the difference as 0.06 nm,. The final i j for RNA is 0.515 ml/g and for DNA is 0.529 ml/g assuming a unit weighting of the four bases Atomic composition Components Phosphate Ribose Deoxyribose Adenine Uracil Thymine Guanine Cytosine

Exchangeable protons

NaPO, C5H703 C5H702

C5H4N5 C4H3N202 C5H5N202

c 5H4 N5 0

C4H4N3O

Ribonucleic acids Adenosine A

C10H11N506PNa

Uridine U Guanosine G Cytidine C

C,HloN,O,PNa 1 ' 0 H l l N 5 O7 PNa C,H,,N,O,PNa

Electrons

Z b (fm)

50 61 53 69 57 65 77 57

26.132 24.473 18.669 65.287 45.786 44.953 71.091 45.640

26.132 34.886 18.669 86.113 56.199 55.366 102.330 66.466

180 168 188 168

115.892 96.391 121.696 96.245

147.131 117.217 163.348 127.484

(H2O)

Volume (2H20)

Electron density

Matchpoint (% 2H,0)

60 125 115 114 99 126 119 103

833 488 460 605 576 516 647 553

71 41 31 122 88 67 151 101

299 284 304 288

602 592 618 583

(X

lov3 nm3)

mean 599 & 15

75.0 63.5 81.6 66.4 71.6 f 8.3

Deoxyribonucleic acids

Adenosine Thymidine Guanosine Cytidine

A T G C

CloHl,N505PNa CloH12N,07PNa C,,Hl1N5O6PNa C,Hl,N306PNa

2 1 3 2

172 168 180 160

110.088 89.754 115.892 90.441

130.914 100.167 147.131 111.267

289 301 294 278

595 558 612 576 mean 585 It 23

70.0 53.5 76.3 61.4 65.3 f 10.0

r W wl

TABLE 6 Scattering properties of some lipids. The electron densities correspond to unhydrated residue volumes

Chemical group Methylene Methylene-d2 Phospholipid headgroup Triglyceride headgroup

Atomic composition

Exchangeable protons

-CH2-C2H2-

0 0

ClrJHl8NO8P C6H506

Phospholipid Dimyristoylphosphorylcholine (DMPC) C36H72N08P DMPC-d,, (96.2% deuteration)

Electrons

-

Z b (fm)

U

Volume

(ml/g)

(X

nm3)

Electron Neutron density match( e . ~ m - ~ ) point (% 2H20)

(H2O)

(2H20)

8 8

-0.833 19.993

-0.833 19.993

1.16 1.16

21 27

296 296

3.6 114.4

0

164

60.086

60.086

0.68

350

469

32.7

0

89

56.020

56.020

0.84

240

371

41.6

0

374

30.944

30.944

0.969

1089

343

12.1

0

374

571.879

571.879

0.969

1089

343

83.4

Dilauroylphosphorylethanolamine (DLPE) ‘29 5SN08

3

318

36.775

68.014

(0.969)

932

341

14.4

Cholesterol Free cholesterol Cholesterol ester (oleate)

C2,H,0 C,,H7,02

1 0

216 364

13.249 19.027

23.662 19.027

0.99 1.08

636 1168

340 312

10.2 10.4

Trigbcerides Trioleate form

C57H10406

0

494

24.763

24.763

1.10

1617

306

10.3

Sphingomyelin Palmitate ester

C3,H7,N206P

2

390

22.495

43.321

1.00

1166

334

11.1

‘36

H2,2H52

159

TABLE 7 Scattering properties of some detergents. The electron densities correspond to unhydrated residue volumes Atomic composition Polyethylene lauryl myristyl ether (Cemulsol) C31H64010 Polyoxyethylene -(CH2CH20),Alkyl chain -(CH2LPartly deuterated Cemulsol * '31H

B Volume Electron MatchExchange- Elm- X b (fm) able trons (ml/g) (X10-3 density point (H,O) (2H20) protons nm3) ( e . ~ r - ~(8'H2O) )

0

330

24.733

0

24

4.138

0

14

330

20.42 H43.601'

930

355

11.9

61

393

17.8

1.26

27

296

3.6

478.740 478.740 0.94

930

355

82.0

940

364

16.9

1.122

427

304

5.5

-0.833

24.733 0.94 4.138 0.834 -0.833

Triton X-100 1

342

0

130

C24H3904Na

2

226

40.522

61.348 0.778

536

422

20.0

Sodium taurodeoxycholate C,,H,O,NSNa

3

282

58.969

90.208 0.76

657

429

22.5

C33H60010.5

55.905

66.318 0.907

N,N-dimethyldodecylamine-N-oxide (DDAO) C14H31N0

-7.684

-7.684

Sodium deoxycholate

* A mixture of 23% fully protonated, 12%in the alkyl chain deuterated, and 65% fully deuterated, in molal ratios of 0.247 :0.123 :0.630.

electron density of the phosphates and carbohydrates is greater than that of the bases. These considerations cannot be easily extrapolated to a folded structure such as that of transfer RNA. Neutron scattering has shown that transfer RNA has a higher scattering density on its surface than at its centre (Section 4.6.2). Lipids and detergents can be considered in terms of polar headgroups and non-polar tails (Tables 6 and 7). This group has the lowest content of solvent exchangeable protons. The range over which pF(r) for the alkyl and phospholipid and that between components in lipids can vary is 30% 'H,O or 170 e . mP3, 40% 2 H 2 0 or 70 e .nmT3 (Table 6). the alkyl and triglyceride headgroup is 100 e . n n C 3 For polyoxyethylene detergents, this range is 15% 2 H , 0 or (Table 7). In all cases the scattering density is higher in the polar domain than in the non-polar domain. For detergents, it is, however, possible to synthesize detergents that are (1) deuterated in the alkyl chain only, or (2) fully deuterated. The appropriate mixture of hydrogenated, partly deuterated and fully deuterated forms has a homogeneous neutron scattering density (Table 7), thus avoiding the compli-

-

-

-

-

-

-

160

cation of the pF( r ) term in scattering analyses of multicomponent systems containing detergent. 2.4. The Guinier plot: I ( 0 ) and R ,

2.4.1. The innermost scattering curve Having discussed the scattering density element of the Debye equation, the geometrical term can now be considered. Sections 2.4, 2.5 and 2.6 deal with only particles that have a uniform scattering density within their surface boundaries. Density fluctuations are dealt with in section 2.7. In a small Q range close to zero Q , the Debye equation is reduced to a simple form, a Gaussian curve. This is shown by the expansion of the term containing sin(rQ)/rQ as a power series:

F 2 ( Q >=

c Cf,f,(l P

4

-

r2Q2 +--r4Q4 5!

r6Q6 + ...) 7!

The first term is ( X pf,)’ or F 2 ( 0 ) ,the square of the structure factor of the particle at zero Q. The second term can be described (see Fig. 1) if the centre of mass of the electrons (or nuclei) in the particle is located at a point 0 such that Xjp . OPp = 0. Hence the vector r 2 can be expanded to give: r 2 = I OFp I + I OQ,

I ’- 2 I OppI I OQ, I cos GPq

For the whole particle, it turns out that the terms in I OP, equivalent while the angular term averages to zero. Hence:

P

=

1--c

1(

?(Q)=(Ef,)

( ?f,)’il

Q2

f~IoPpl2

* P

-

I and 1 OQ, I are

+

EfP P

+ ...)

where the radius of gyration R , is defined in analogy to classical mechanics as:

R&=C P

fp

I opp I EfP

P

This leads to the well-known Guinier relationship [6] (Fig. 4). The experimental In I ( Q ) data are plotted against Q 2 to give a straight line of slope - R & / 3 and intercept In I ( 0 ) : In I ( Q ) = In I ( 0) - R&Q2/3

161

-3 0.00

0 04

0.08

0.12

C 16

Q' (nm-2)

Fig. 4. Guinier plots of In Z(Q) u . Q 2 and the Q . RG range of validity for a sphere, a prolate ellipsoid of axial ratios 1 :1 : 1.8 or an oblate ellipsoid of axial ratios 1 :1 :0.24, and a long rod, each of RG 5 nm. The Guinier relationship is valid in the Q . R , range from 0 up to 0.7 for rods and to 1.3 for spheres.

I ( 0 ) is the intensity at zero scattering angle and is proportional to M,'. The RG value characterizes the degree of elongation of the structure, and can be compared with similar shape parameters such as sedimentation and frictional coefficients. In principle, R , and I ( 0 ) data are model-independent parameters, i.e. requiring no presumptions about macromolecular shapes. Guinier plots are valid only at low Q when the third and higher terms in the series expansion are neglible. The lowest Q values are, however, not measurable for reason of the main beam and the beamstop. For a given particle, the smallest Q that where has to be measured to give RG is given by the relationship QminDmax 1.3. At the other shape extreme of long rods, these break down when Q . RG > 0.7. Certain intermediate shapes satisfy the Guinier plot up to the sixth power of Q in their series expansion, i.e. their scattering curves remain Gaussian in larger Q ranges. These shapes include oblate ellipsoids of axial ratios 1 : 1:0.24, prolate ellipsoids with an axial ratio of 1 : 1: 1.8 and cylinders of height : diameter ratio 1.65 : 1. All these are mildly elongated particles. Accordingly, many globular proteins can satisfy the Guinier plot up to the fourth power of Q since these are of a similar elongated nature (Section 4.2.1). It is useful to note from Fig. 4 that the calculated curves for rods or spheres rise above or diminish below the Gaussian line at large Q values when the Guinier plot breaks down. For these shapes, and more complex ones (such as toroids, or bundles of cylinders joined together at one end), simulations using an assembly of Debye spheres or uniform shape models can help to assess systematic errors that are introduced in Guinier analyses by the actual Q range in use [39]. In general, sufficiently accurate R ,

162

values are usually obtained if there are sufficient data below Q - RG G 1-1.5. In practical terms, RG values need to be substantiated by correct molecular weight calculations from I ( 0 ) values, and the actual Q range used for RG values should be specified. Concentration series down to 2-5 m g / d are required to establish the reproducibility of the RG measurement and to eliminate the possibility of interparticle interference or non-specific aggregation phenomena. 2.4.2. Cross-sectional and thickness Guinier analyses Two other Guinier-type analyses are possible for rod-like and platelet-like lamellar particles. If one dimension of a particle is large compared with its other two dimensions, the scattering curve can be divided into two factors that reflect ( 1 ) the total particle length and depends on l / Q and (2) the cross-sectional area. The former is investigated by means of Guinier plots subject to the Q . RG < 0.7 condition. Since the scattering contribution from the total length will rapidly diminish to zero as Q is increased, the scattering curve at larger Q will reflect the cross-sectional property of the particle. For a rod-like particle with length L, the total scattered intensity I(Q ) is related to the cross-sectional intensity, Ixs(Q ) by I(Q ) = 7rL - Ixs(Q )/Q. Multiplying the scattering curve I(Q ) by Q eliminates the length factor, and the cross-sectional radius of gyration R,, is obtained from cross-sectional Guinier plots (sometimes called Porod plots) [40]:

Cross-sectional R x s analyses can be performed on particles whose lengths are only a few times larger than the other dimensions, even if the diameter :length ratio is as low as 1 :2, although at this limit the region of the scattering curve amenable to this analysis is restricted. Molecular weights per unit length can be calculated from [ln(I(Q)- Q ) ] Q - o .Combination of the RG and R x s analyses give the length L of the rod:

The consistency of these two calculations is an important control of a correct cross-sectional analysis for a rod-like particle [41]. For lamellar particles, where two dimensions are large compared with the third dimension T, the thickness, similar considerations apply. The curve I ( Q ) can be separated into an area factor depending on l / Q 2 and another that reflects the thickness factor, which is again a Gaussian function. Thus I ( Q ) = 27rA . ITH(Q)/Q2. Multiplication of I ( Q ) by Q 2 eliminates the area factor, and a thickness Guinier analysis (sometimes called Kratky-Porod plots) gives the thickness radius of gyration R T H :

Particle thicknesses can be determined for lamellae even if the length and the width

163

of the particle are only about 2 or 3 times larger than the thickness. However, the precision of thickness analyses is not usually as great as those for determining cross-sectional properties. The value of R , H gives T from:

T=

m~,,

Molecular weights per unit area can be calculated from [ I ( Q ) .Q 2 ] Q + odata. 2.5. Analyses of I ( 0 ) values I ( 0 ) values give information on the chemical composition of the particle, in particular the molecular weight. Starting from the Debye and Guinier equations, and allowing for solvent,

I ( O ) = ( Cfp-psV)

=Ap2V2

I ( 0 ) is thus proportional to M,‘ since C, fp and V are each proportional to M,. A plot of (where I ( 0 ) has been normalized for sample thickness t , concentration c and transmission K ) against solution scattering density ps is linear, from which C, fp and V can be determined. In neutron scattering when the particle can readily be matched-out by solvent, I ( 0 ) is zero when C,fp = psV. Since this matching involves the use of H,O and ’H20, the effect of the hydration shell surrounding the particle in solution on the volume is largely circumvented and so the “dry” volume is determined. Exchangeable protons within the particle can be assumed to exchange freely with the H 2 0 and 2 H 2 0solvent, except in the case of globular protein structures. Neutron protein crystallography and protein ‘H nuclear magnetic resonance indicate that about 10-20% of main-chain peptide NH protons do not exchange for reason of their location within stable secondary structures [37]. “Wet” volumes are derived by methods which involve the presence of additives in the buffer that do not penetrate the hydration shell. For X-ray and neutron scattering, sucrose or salt is added to the solution for this purpose. Molecular weight calculations can be carried out in any contrast ps by allowing for the term in psV. For a sample of known concentration c (mg/ml), the number of particles N is proportional to c/M,. Thus I ( 0 ) a M ; * c/M, or I ( O ) / c a M , . In a given scattering experiment set-up and using the same buffer, I ( 0 ) values for different samples can be normalized using sample concentrations c, giving I ( O ) / c terms that are proportional to M, and leading to relative M, values. Calibration using a sample of known M, and c and with a comparable Guinier Q range will give absolute M, values. Kratky’s equation [lo] gives absolute M , values by relating M, to the total of scattering lengths (electrons or nuclei) in the particle. In X-ray scattering, if the total of electrons in the particle Cf (containing zN, electrons per gram: N, is Avogadro’s

{m

164

number) is zM,, then Thomson's equation for the scattering due to a single electron becomes

-(

I ( 0 ) = e4

L)z2M: m2c4 SD2

If the irradiated sample area is a and the sample thlckness is t , then for a sample concentration of c mg/ml, the sample mass is atc. The total of particles present is atcNJM,. The total intensity received on the irradiated sample area can be written as 2 Z P / a . In order to allow for the solvent contrast when the particles of partial specific volume U are immersed in a solvent of electron density p s , z is replaced by ( z - 5. ps/N,) to correspond to the effective number of mole-electrons per gram of solute. Thus the final expression for I ( 0 ) is

In practical terms, the ratio I ( 0 ) / 2 2 P has to be measured. Since this is very low, this task requires the use of calibrated filters to reduce the intensity of Z E P , or that of standard X-ray scatterers such as calibrated Lupolen. In neutron scattering, the use of Kratky's equation is much simplified by using the strong incoherent scattering from water as the absolute standard [42]. This replaces the calculation of I ( 0 ) / 2 2 P above. For a water sample that is 1 mm thick and is irradiated with neutrons of wavelength > 1 nm, the incoherent scattering Iincoh is uniform in all directions and corresponds to about half the intensity of the incident beam distributed over 4s.However, for wavelengths < 1 nm, the recoil of nuclei in collisions with neutrons is stronger in the forward direction and has an angular dependence. Corrections are required here. When the primary beam of total intensity P per unit irradiated area is incident on a water sample of area a and transmission T,, the neutrons uniformly scattered into the solid angle D measured on the detector is given by:

f2

Iincoh = -(1 - T, ) Pa 4s while T,Pa neutrons pass through the water sample (note that with water, no neutrons are lost through absorption processes, unlike vanadium which is also a good incoherent scatterer). The solution of particles (transmission T,) will transmit T,. P . a neutrons. The geometrical term in neutron scattering is T, . P .D,and on substitution it becomes Iincoh4sT,/(1- T,)a. The final expression for I ( 0 ) is thus:

where z above has been replaced by the term Z b / M , which is common in neutron

165

scattering. An anisotropy factor A , has been incorporated to allow for neutron wavelengths < 1 nm. This diminishes from 1.0 for X = 1.0 nm to 0.461 for A = 0.1 nm. The transmission of a 1 mm thick water sample at ambient temperatures decreases from 0.57 for X = 0.5 nm to 0.46 for A = 1.0 nm and 0.39 for A = 1.4 nm. The determination of M, is dependent on the value used for U , which is not necessarily well-determined (Section 2.3.2). The U enters the calculation as the square of a difference. Thus a 1%error in U leads to a 4 - 5% error in M, by X-ray scattering. Since in neutron scattering the value of ps for H 2 0 buffers is small (Table 2), a 5% error in U now leads to a 1.5%error in M,. T h s shows that neutron scattering in H 2 0 is more reliable for M , determinations, despite the disadvantage of the high incoherent scattering background in H 2 0 buffers, which means that lengthy counting times are required for satisfactory signal-noise ratios. In ' H 2 0 solutions, neutron scattering gives I ( 0 ) values that reflect both the M , and the U of the particle. In the case of proteins where incomplete 'H - H solvent exchange is also a factor, I ( 0 ) also reflects the degree of 'H non-exchange. Experimentally, I ( 0 ) values are recorded, which are then normalized by the concentration c. Accurate M , determinations also rely on concentrations, as determined by optical densities or other methods. The significance of a good M , calculation is that it provides an important quality control for the scattering experiment, subject to errors arising from 6, c and 'H - H exchange. Cross-sectional M, values per unit length L and thickness M, values per unit area A can be derived from their corresponding Guinier analyses. For rod-like objects,

For platelet-like objects,

2.6. Analyses of R , values

The RG corresponds to the mean square distance of scatterers from the centre of gravity of Scattering lengths. In practical terms, it is a measure of the degree of elongation of the particle. The most compact shape for a particle is a sphere, and, if its RG is denoted R,, knowledge of M, and V for the particle enables the R , for the sphere to be calculated (Table 8) [10,25]. The ratio of R G / R , quantifies the particle elongation, by analogy with the use of frictional ratios f / f 0 in sedimentation or diffusion experiments. Measured RG values can alternatively be assessed by comparison with the R , values for a known family of shapes, such as typical globular proteins [25] or transfer RNAs. The RG values are rescaled on the basis of

166

TABLE 8 Radii of gyration R , for simple bodies Sphere (radius r )

R2 - 3

Hollow sphere (radii r,, r2)

R2

Ellipsoid (semi-axes a , b, c)

R&=

Prism with edge lengths A , B, C

R& =

Elliptic cylinder (semiaxes a , b and height h )

G-TT

2

3 r; - r:

,5 r;-r;

a ’ + b2

+ c2

+ B~ + c2

12 a ’ + b2 h2 R 2 --

4

G -

+iz

a’+ b2

R2,,=_ Hollow cylinder (radii r l , r2 and height h )

R2

’

- r2+r2

h2

G - T + E

+ r; xs - 2

R2 - r 2

the cube root ratio of M , values. Alternatively, if the particle is assumed to be an ellipsoid, calculations based on the RG value (Table 8 ) and the known volume will give the axial ratios of the oblate and the prolate ellipsoids corresponding to the observed RG. Further RG analyses can be carried out to investigate conformational changes in the particle, binding equilibria between different particles, and comparisons with known macromolecular crystal structures. The Parallel Axes Theorem is useful to study oligomer formation or the fragmentation of a particle, since it yields the separation A between the two subunits in the object of interest:

where f A and f B are the volume fractions of subunits A and B in the complex C , with the corresponding RG values denoted by the subscripts. This equation assumes no conformational change has occurred in the formation of the complex. In the study of mixtures of particles, the Guinier equation becomes the sum of contributions from all components. The mean R , is a z-averaged value and is given for P conformers, each with an RG denoted RGp, by:

where the terms in f p correspond to the total of scattering lengths in each particle, and the terms in x p reflect the proportion of each particle in the mixture. Since large RG values are favoured in the average, sample contamination by small

167

amounts of non-specific aggregated particles has a serious effect on the Guinier analyses for RG and Z ( 0 ) . Note that dust particles in the samples do not have this effect since they are too large to be seen in X-ray or neutron scattering (unlike in light scattering). The corresponding average I ( 0 ) value of the mixture is a weightaveraged value:

Since Z ( 0 ) is proportional to M,?, the presence of aggregates is again seen to be serious. Scattering curve intensities in the Guinier plot are no longer linear in the In Z ( Q ) v . Q 2 plot but curve upwards as Q decreases. If a crystal structure is available for the macromolecule, the experimental RG may be compared with that calculated from the crystal structure. For an atomic model containing n coordinates, n

where f p are the scattering length and rp is the distance between the coordinate and the centre of scattering of the particle. The crystallographic model can alternatively be converted into overlapping spheres using a cut-off scheme so that the total volume of the spheres is equal to the volume of the macromolecule, and the volume of each sphere reflects the cube used to section the atomic coordinates. For this, or for other arrangements of spheres derived from techniques such as electron microscopy, the RG can be calculated using:

k= 1

where each of the n units has a RG denoted as R , and is set at a distance r, from the centre of mass of the spheres. 2.7. Non-uniform scattering densities and contrast variation

2.7.I . The Stuhrmann plot In general, biological macromolecules do not have uniform scattering densities, either within a gven macromolecular class (Tables 3-7), or within a multicomponent system (Fig. 2). An explicit consideration of this requires the decomposition of the scattering density of a particle p ( r ) in excess of solvent ps into the sum of terms based on the overall shape p v ( r ) and density fluctuations p F ( r )(Fig. 2 ) [14,43]: - Ps = A P . P v ( r ) + P F W

168

The contrast Ap is the difference between the average particle density and the solvent, i.e. pv-ps. The step function pv(r) is 0 outside the particle and 1 within the particle boundaries, and corresponds to the volume that excludes solvent molecules. At high Ap, pv(r) is dominant, and at low Ap, p F ( r ) is dominant. Contrast variation methods permit the separation of the p v ( r ) and pF(r) terms by varying Ap. Fourier transformation of the excess scattering density p ( r)-ps gives the amplitude A ( Q ) and this has the same contrast dependence as above:

Multiplication by the complex conjugate gives the scattering curve I ( Q ) as a parabolic function in Q and Ap :

Thus measurements of I ( Q ) as a function of n contrasts enables the three unknowns, Iv(Q), IvF(Q) and IF(Q) to be determined at each Q value. In that order, they are termed the three basic scattering functions from the shape, the cross-term and the fluctuations. See Section 4.6.4 and Fig. 28 below for their application to chromatin. I v ( Q ) and I F ( Q ) are true intensities which are always positive, whle IvF(Q) can be positive or negative. Combination of the definition for R , with that for p(r) gives the dependence of R , on Ap. This leads to the Stuhrmann equation (44):

where

1

a = -j p F ( r ) r 2 d 3 r

VC

vc -- 1 p v ( r ) d 3 r Stuhrmann plots of R& versus Ap-' gives R , , the radius of gyration at infinite contrast (Fig. 5). The tangent to the curve at Ap-' = 0 gives a and this reflects the

169

j’ b

40

E I

20

N O w -[L

C

matchpoint of P

0 -2

0

2

-2

0

aP-l x lo4

2

-2

0

2

nrn-2

Fig. 5. Schematic Stuhrmann plots for two-component systems. (a) If the two components are concentric, a linear relationship is found between R& and A p - l . The slope a is positive as shown if the outermost component has a higher scattering density than the innermost component. It is negative if the lower scattering density is on the outside. Data collected in buffers with *H,O contents below the matchpoint lie in the positive A p - ’ range. (b) If the centres of the two components are separated within the macromolecule and their matchpoints are sufficiently different, the curvature of the plot represents the separation between the centres of the two components. The value of a can be positive, zero or negative, while p is zero or positive. (c) Stuhrmann plots for a two-component system M + P and M + D , in which component P of lower matchpoint than M has been isomorphously replaced by deuterated D with a higher matchpoint than M. The value of R , for each of M and P / D are obtained by intrapolation as shown.

radial distribution of scattering density fluctuations. Note the similarity in the definitions of R: and a, although a is dimensionless in neutron scattering as is apparent from Fig. 5. Since p F ( r ) is weighted by r2, the sign of a will be determined by the scattering density in outer regions of the particle. If the particle can be approximated by an inner sphere and an outer concentric shell, a is positive if the shell has a higher scattering density than the inner sphere (Fig. 5a). Examples include glycoproteins, lipoproteins and chromatin core particles. It is negative if the inner sphere has the higher density, and examples include ribosomes and viruses (Section 4). For two concentric distributions 1 and 2, each of uniform density p1 and p2 and values V, and V,, a is given by [45]:

where R , and R , are the R , of each distribution and p is the mean density. In the case of two non-concentric distributions whose centres are separated by A, a is given by [46]:

170

For an assembly of n spheres, a is given by [39]:

where pk is the scattering density of the unit k, pv is the mean density and rk is the separation between the unit k and the centre of the spheres. The term p reflects the curvature of the Stuhrmann parabola and is always positive (Fig. 5). Since it is a second-order term and is defined mainly by R& values measured in low Ap (where counting statistics are usually weaker and sample impurity effects are larger), the inherent accuracy of /3 is less than that of R , and a. Physically, it corresponds to the displacement of the centre of scattering within the particle as the contrast is varied, i.e. p corresponds to the distance between the centres of the shape pv(r) and the fluctuations pF(r). Typical systems where p might be measurable include protein-detergent, protein-nucleic acid and protonated-deuterated protein complexes (Section 4). If a particle can be divided into two components 1 and 2 with distinctly different scattering densities, the separation between 1 and 2 can be calculated [47]:

This expression is identical with the Parallel Axes Theorem above, even though the two components have been distinguished by contrast variation and not by chemical separation into separate entities [48]. This identity is readily shown by equating R,, and R,, in the Parallel Axes Theorem with the R , values in the Stuhrmann plot at Ap values that correspond to the matchout of components B and A respectively, i.e.

2.7.2. Solvent penetration and exchange effects In the application of the Stuhrmann plot to X-ray scattering, Ap is varied by adding sucrose or salt to the sample buffer. In the sense that these additives do not penetrate surface hydration shells or inner hydration domains, p v ( r ) and pF(r) can be interpreted in straightforward molecular terms of the hydrated shape. In neutron scattering, however, the variation of Ap using H,0-*H20 mixtures implicates solvent-solute ‘H-2H exchange phenomena, both at exchangeable proton sites in the macromolecule and in hydration domains. The effects of this on both p v ( r ) and pF( r ) require consideration. Since exchange causes volume elements within the particle surface to have identical properties with the solvent (i.e. resembling voids), pv(r) can be 0 at a number of sites within the particle, and on average p v ( r ) will be less than 1 [MI. Fig. 2 shows that exchange influence pv(r) for proteins, carbo-

171

hydrates and nucleic acids (which increases with buffer 2H,0 content) but less so for lipids. Exchange also causes effects in p F ( r )if differential 'H -* H exchange occurs in different regions, which causes the relative magnitudes of the fluctuations throughout the particle to depend on the contrast. Binary systems of lipid-protein (no exchange in the lipid component) or protein-hydrated RNA (hgh exchange in the RNA component) constitute two extreme examples. Both these effects can be considered by rewriting p ( r ) - ps as:

Note that the term in Ap allows for change in p v as a function of ps due to exchange. The step function p E ( r )represents the position and density of exchangeable protons. There will in principle be another term pEF(r) which reflects the internal fluctuation of the density of exchangeable proton sites. This will modify p F ( r )in a manner dependent on Ap; however, this is not considered further. Expresssions for solvent penetration effects can be derived [a]. The effective particle volume Vc is given by:

The term (1- u ) is a loss factor. The value of u is usually estimated from the ratio of exchangeable protons within the physical volume Vv to the total exchangeable protons in the same volume of water. If hydration shells are not taken into account, typical neutron (1 - u ) values are 0.81 for proteins (0.89 for hydrophobic residues; 0.72 for hydrophilic residues), 0.77 for carbohydrates, 0.85 for RNAs, 0.90 for DNAs, and 0.99 for lipids. For X-rays, (1- u ) is close to unity. The other Stuhrmann constants are expressed as:

a

= R2,-2mE.mF

with the positions of the centres of p E ( r ) and p F ( r )given by m E =- 1J P E ( r ) . r d 3 r VC

m F = -1 JpF(r)-rd3r VC

172

and the radii of gyration by:

~2

- -JpE(r)r2d3r 1 E-

v,

The centre of the particle volume is chosen as the zero point for r . If the centre of pE(r) coincides with that of pv(r) then mE averages to zero and

R2, =

R; - u R ~ 1-24

-

If (1 - u ) is taken as 0.81 for globular proteins, and if Ri R ; , the presence of voids due to exchange within the particle surface can be readily estimated to have a small effect on R $ , a and p. Since in fact the V, values from matchpoint determinations are close to Vv values calculated from atomic compositions, the experimental value of (1 - u ) is close to unity, at least in the cases of proteins and glycoproteins. Here, it would appear that the effect of ‘H exchange on neutron R,, a and P values can be ignored. In the cases of the spherical, iSometric viruses which have heavily hydrated RNA or DNA cores, the effect of ‘H - H exchange means that these shapes are more correctly described at infinite contrast in terms of geometrical hollow shell models, whose R , value is thus larger than that of the corresponding uniform sphere of the same diameter (see [49,50]). 2.7.3. Isomorphous replacement The deuteration of specific components in a multicomponent system at non-exchangeable sites causes large changes in p v values, and the resulting system can be analysed by contrast variation. In a given two-component system, the Stuhrmann plot can be used to determine R , values for each component at the Ap value corresponding to the match-out of the other component. The residual density fluctuations of the matched-out component will however contribute to the measured R , value and this can lead to significant errors. Ths difficulty can be circumvented by isomorphous deuteration of one of the two components in order to increase its matchpoint to a value greater than that of the other component, and repeating the Stuhrmann study [39,47]. Two R k values for each component are thus obtained (Fig. 5c). By linear intrapolations of the two Stuhrmann parabolas, the R , values at

173

infinite contrast can be calculated for each component. In this way, density fluctuation effects have now been largely avoided. 2.7.4. Matchpoints of multicomponent systems Matchpoints in a two-component system denoted 1 and 2 can be calculated from a graph of 2 b - p s . V against ps, where 2 b is the sum of coherent scattering lengths, V is the total volume, and X is the volume fraction matchpoint [39]:

- pH20Vl

'bl,H20 XL2 =

(2 b l , H 2 0

- PH20vl)

Xl

+2b2,H20

+ (2b2.H20

-pH20&

- PH20VZ)

XZ

From a graph of 2 b against ps, the following can be derived:

-

tzb1,H2O

+ 2b2,H20)(1

PVl.2 -

- x1,2> + (2b1,2H20 + 2b2,2H20) Vl +

x1,2

v,

Alternatively the simpler relationship can be derived:

where pv,,2 is the scattering density at the matchpoint Xl,z and pv, and pv2 are the scattering densities. 2.8. Label triangulation The deuteration of specific components in a multicomponent system at non-exchangeable sites can be employed in neutron techniques that employ interference analysis by label triangulation to determine the distance between two deuterated subunits withm a macromolecular complex [51]. The deuterated subunits are incorporated into the complex by reversible dissociation and reconstitution experiments. The method can also be applied to two protonated subunits that have been reassembled in a deuterated matrix, as would be expected from Babinet's Theorem. In the case of X-ray scattering, deuterated labels are replaced by a suitable heavy atom label such as a cluster of four Hg atoms covalently bound to cystine SH groups. The scattering from these labelled groups can be considered using the Debye equation rewritten in terms of the scattering from the labels 1 and 2, the matrix 3 and the cross-terms between 1, 2 and 3 [22]. For the unlabelled particle:

174

If deuteration uniformly changes the proton scattering length from bp to xbp, the equivalent expressions for the particle with group 1, group 2 and both 1 and 2 deuterated are written, respectively, as:

If the scattering curves are measured in these four cases at equal sample concentrations, the interference term between groups 1 and 2 can be isolated by taking the difference: (I,

+I,)

- (I,

+ I,)

=

(2- 2 x ) I , ,

This method requires low sample concentration in order to avoid interparticle interference effects. However, if an equimolar mixture of unlabelled and bilabelled particles (A + D) and an equimolar mixture of the two singly labelled particles (B C) are measured, subtraction of the two scattering curves permits I,, to be measured at high concentration since the interparticle effects are eliminated [52]. T h s is important for the triangulation of subunits in large systems such as the ribosome, since otherwise the label concentration becomes extremely low. The interference function Z12 is similar to the scattering curve of a simple diatomic molecule I12(Q)[23]:

+

= b:

+ b i + 2b,b2 sin I rl - r, I Q I ri - r2 I Q

Since this function is zero at multiples of TQ (Fig. 6), the separation A between the labelled subunits (i.e. the term in Ir, - r2 I) is given directly by n / v Q , where n is an integer [53]. For molecules whoses shapes deviate from spherical symmetry, the positions of the zeroes of I,, can be affected and more detailed analyses are required to interpret the results. Modelling based on ellipsoids show that the effect of shape on the distance measurements is small and that the most reliable method for obtaining A (to within 10%) is to determine the position of the first zero of the interference ripple, where n = 1 [54].By successive reconstitution and I,, measarements, it is possible to analyse A for all pairs of subunits within the structure. By triangulation, the quaternary structure is derived. For n subunits the total number of distances between these is ( n , - n ) / 2 , while (4n - 10) distances is sufficient to define their arrangement. There is much redundancy and accordingly more distances than are necessary can be measured in order to optimize a best fit for the

175 5 r

4-

-a

3-

--

-

2

1-

0

,

quaternary structure. Further aspects of triangulation are considered in Sections 4.3.2 and 4.6.5. 2.9. Wide-angle scattering and modelling strategies 2.9. I . Spheres and ellipsoids X-ray and neutron scattering curves measured beyond the Guinier region lead to further shape information in addition to RG values. Theoretical curves calculated from simple models of uniform density illustrate t h s (Fig. 7). Thus for a sphere, the scattering curve is gwen by [6]: I ( Q )= 3

(sin QR - QR cos Q R ) ~

= @’(QR)

(QR)’

The term G2(QR)is the squared form factor for the sphere of radius R. For a hollow sphere of outer and inner radii R , and R , [7]: sin QR, - QR, cos QR, (QR,)’

- R:

sin QRI - QRI cos QRI

( Q R1’~

The scattering curve of a sphere descends into a series of minima and maxima as Q increases, with the first minimum at QR = 4.493. Thus the RG of the sphere can be calculated from the minima as a verification of the Guinier analysis. The curves for full and hollow spheres are very similar at low Q. The intensities of the subsidiary

176

0

-a

-4

-C

-8

-12

-16 1

2

3

4

1

2

3

a (nrn-5 Fig. 7. Scattering curves from models of uniform scattering density. (a) A sphere of radius 6.5 nm and R , 5.0 nm as used in Fig. 4. (b) A hollow sphere with an outer radius of 6.5 nm as in (a) and a ratio of inner/outer radii of 0.5. (c) A straight, cylindrical rod of length 59 nm and diameter 3.4 nm. (d) The cylindrical rod as in (c) is now bent into a circle of radius 9.4 nm.

maxima, however, differ markedly, in direct reflection of the size of the cavity relative to the size of the particle, i.e. on the ratio of R, to Ro. These analyses are useful for ferritin (Fig. 17), lipoproteins (Section 4.5.3) and viruses (Section 4.6.6). Scattering curves for prolate and oblate ellipsoids can be calculated. For an ellipsoid of revolution of axes 2 a : 2a: 2ua [6]:

This expression is an adaptation of the Z(Q) calculation for a sphere and the required integration can be performed numerically. Particles that do not have spherical or near-spherical symmetry do not exhibit the minima and maxima noted above, and the scattering curve Z(Q) declines more uniformly as Q increases. Other analytical expressions exist for the calculation of I(Q) for ellipsoids, prisms and cylinders and their hollow equivalents [55]. It should be noted, however, that Z(Q) for ellipsoids, prisms and cylinders do not differ greatly. For simple models, a first indication of the macromolecular shape in terms of a triaxial body can be extracted by curve-fitting of the calculated scattering to the experimental curve at low Q.

177

2.9.2. Scattering curves at large Q At large Q , Z(Q) will reach a finite value, as expected from the Debye equation. By Porod’s Law, there is a Q P 4 dependence of Z(Q) in a region that corresponds to 1 - 2 nm resolution, provided that the mean particle-solvent contrast A p is large compared with that of the internal structure pF(r):

where S is the surface area of the particle. Additional quantities can be calculated, given a complete scattering curve, most notably the particle volume. The invariant of the scattering curve Inv is calculated from the integral: M

Inv = J, Q2Z(Q)dQ= 2 ~ ~ ( d p ) ~ V Physically, this integral corresponds to the sum of excess scattering densities, irrespective of the particle shape. Thus for a given particle size, the integral must remain invariant, even though its shape may change. Remembering that I ( 0 ) = Ap2 - V 2 ,the particle volume is determined from: V=

2&(0) Inv

Since the calculation of Inv requires the product of low-intensity I ( Q ) values with Q 2 at large Q , V cannot be well determined. Integration is performed numerically using Simpson’s rule up to a suitably large Q of 3 nm-’. The remaining 10% of Inv is obtained from a Porod Law plot of I ( Q ) v . QP4, where the experimental curve will oscillate about a straight line whose slope k can be determined for use in The value of V can be compared with curve extrapolation based on I ( Q ) = that obtained from M , and 5, where V = 6 . M,,”,. For rod-like particles, an analogous expression exists for the cross-sectional area A:

-

Icep4.

and likewise for the thickness T of lamellar particles:

The accuracy of the [Z(O). Q ] Q + ~and [ I ( 0 ) .Q 2 ] Q + ovalues is, however, not high.

178

Scattering curves Z(Q) give other structural parameters which are less directly related to the particle shape than the values of R,, I ( 0 ) (= M,), and V. One is the correlation length L, which corresponds to the number average of the lengths or chords which can be drawn to join all points on the surface of a particle in all directions:

L,

=

n l w ~ ~ ( ~ ) d ~ Inv =2imy(r)dr

In analogy to the invariant, L, can be calculated from integration of Z(Q). L, is also related to the correlation function of the particle y ( r ) (section 2.10) since L, corresponds to its mean width. Another scattering parameter is the specific surface S / V , which can be calculated from Porod's Law above:

From this and V, the surface area can be calculated. 2.9.3. Independent parameters from scattering The maximum ideal number of independent structural parameters J from a solution scattering experiment can be estimated from sampling theory. T h s assumes error-free experimental data that are not distorted by background subtraction or beam smearing or collimation effects. Since the maximum distance D,, of a particle defines its boundary beyond which the particle does not exist, and since the scattering curve is measurable to Q,, (beyond which the intensities are inaccessible or are too weak), the sampling theorem of Fourier transformation gives the number J of independent parameters as Om,. Q n /,, [7,16]. For a sphere of diameter 4 nm and measured to Q = 3 nm-', J is about 4 which would correspond to the determinations of M,, R,, V and S for a protein of M , 30,000. For a sphere of 40 nm diameter measured in the same Q range, J rises to about 40. In a complete contrast variation study that gives the three basic scattering functions Z,(Q), ZvF(Q) and IF(Q), the maximal number of parameters becomes 3J. 2.9.4. Debye curve simulations Modelling strategies based on Z(Q) data are based initially on the values for V (or M,) and R , (Sections 2.5 and 2.6; Table 8), together with the values of R,, and R,, and their related parameters if available, and the maximum particle dimension (Section 2.10). More detailed modelling involves direct comparisons between experimental and calculated Z(Q) curves (Fig. 7). These can involve the use of Z(Q) calculated from simple triaxial bodies (above). The most powerful and general method is to use small Debye spheres in three-dimensional arrangements to refine and extend the curve fits of Z(Q). The shape under consideration can be directly

179

subdivided in terms of spheres, and computer graphics can be readily used to visualize the spheres. Thus Z(Q) is calculated from the Debye equation [56]: -I(')

- # ( Q R ) ( n - ' + 2n-2

I(0)

A,j =1

Qr, Qr,

sin

Here, n is the number of spheres filling the body, A, is the number of distances 5 for that value of j , 'J is the distance between the spheres, m is the number of different distances r,, and +'(QR) is the squared form factor of the sphere (see above). At large Q, R has to be sufficiently low and m sufficiently great that they have no effect on I ( Q ) . For n , and n 2 spheres with different scattering densities p1 and P 2 ,

)'(-I I(0)

- Q2(QR)(n,p:

+ n 2 p ; + 2p:

c A;'-sinQ5Qr, + c A,'"---sinQ5Qr, 2p;

j=l

j= 1

sin Qr. j=l

where A;', Af' and A;' are the number of distances 5 for that increment of j between the spheres 1 and 1, 2 and 2, and 1 and 2 in that order. This procedure is readily extended to consider three densities. The R , and the Stuhrmann (Y can be calculated for the spheres also (Sections 2.6 and 2.7). In the case of a known crystal structure, I ( Q ) can also be calculated, where each coordinate is weighted by a term feff =f- psKff in order to correct the atomic scattering lengths for the influence of the solvent scattering density using the apparent atomic volume V,,,. Alternatively the crystal structure can be converted into spheres (Section 2.6) for a Debye calculation. It is stressed, however, that the coincidence of experimental and calculated scattering curves only proves that the model is equivalent in scattering, and not that the model is unique. Another modelling strategy is based on the use of spherical harmonics, where the excess scattering density p ( r ) - p s is expanded as a finite series of multipoles in order to approximate the shape of the particle [57]. While the experimental and calculated I ( Q ) curves can be compared in this way, it has not yet been shown that the particle shape can be readily visualized in the way that is possible by computer displays of Debye spheres. The calculated scattering curve I ( Q ) may require corrections for instrumental effects due to wavelength polychromicity and/or beam angular distortions. For X-ray cameras that are run on conventional anode sources, desmearing is required at the lowest Q values (Section 3.4) and has been extensively discussed by Glatter [58].Synchrotron X-ray cameras approach an ideal instrumental geometry in terms of wavelength and beam effects and these corrections can be neglected. In neutron scattering, corrections are required for wavelength spread AX/X and beam diver-

180

gence A0 . These can be applied by assuming a Gaussian function G ( Q,Q’) which is used to convolute Z(Q) at each increment of Q over the Q range denoted Q’ [59]. The resulting intensities are summed to yield the smeared curve [39]:

+

where :a = (8 In 2)-’ ((2Q .AA/X)2 (AO. X / ~ T ) ~and ) AX/h and A0 can be determined empirically or by calculation from the instrumental geometry. 2.9.5. Interparticle interference At high sample concentrations, the intensities in Z(Q) are reduced at small Q, and this can lead to artefacts in Guinier plots that exhibit reduced or even negative R& values. The orientations of the particles are correlated with one another, and leads to interparticle interference phenomena. The hard sphere model can be used to calculate ZHS(Q)as a first approximation to the experimental curves [6,7]:

ZHs(Q) =constant - $ ’ ( Q R ) where $ ( Q R ) is the form factor of the sphere of radius R and VJV, is the packing parameter (V, = volume of each sphere; V,: total sample volume per sphere). 2.10. Distance distribution functions Scattering curves I( Q ) reflect the structural properties of particles in reciprocal space. The correlation function y ( r ) (which is related to the Patterson function of crystallography) and the distance distribution function D( r ) represent the particle shape in real space [58]: D(r)=r2.y(r)

For a homogeneous particle, D ( r ) multiplied by 4a represents the number of distances r which are found in the combination of any one volume element p with any other volume element q in the particle. The main advantage of D ( r ) is that Om,, the maximum particle dimension, is readily obtained since D ( r ) drops to zero at r = D,, (Fig. 8). Other advantages of D ( r ) are that it permits calculation of R , and Z ( 0 ) values using the whole scattering curve instead of the Guinier region of the curve at low Q , and that it leads to a qualitative classification of the shape and internal structure of the particle. The disadvantage of D ( r ) is that its computation involves Fourier transformation of the experimental Z(Q) curve for 0 G Q G 00: Z(Q).Qr-sinQr.dQ

Since measurement is limited at low Q by the primary beam and the beamstop, and at large Q by deteriorating signal-noise ratios, termination errors are readily

181

4-

,/\,*

Prolate

r(nrnl

Fig. 8. Comparisons of the distance distribution functions D ( r ) for a sphere of diameter 3.82 nm (),aprolateellipsoidwithaxialratiosof1:3:3andaxes2nm~2nm~6nm~~~~~~~~~),a an oblate ellipsoid with axial ratios of 1 :1 :0.2and axes 4.64 nm X 4.64nm X 0.92 nm (- - - - -). All have the same R , value. From Glatter [7].

introduced. The Glatter or the Moore Indirect Transform procedures are, however, able to minimize these termination effects [58,60]. The corresponding D( r ) functions for the cross-section and thickness of rod-like and lamellar particles are given in that order by:

D x s ( r ) = -/ m ~ x s ( ~ )e .r - ~ , ( e r ) d e 2" 0 where Jo(Qr)is the zero-order Bessel function, and: D T H ( ~ )= ' / m l T H ( ~ )

"

0

-cos(er>d~

The R , , R,, and RT, values can be calculated from:

lm ( ) D r r 'dr

Rg=

182

The I ( 0 ) value is calculated from I ( 0 )=4njWD(r)dr 0

In the case of inhomogeneous particles, contrast variation techniques can be used to separate the shape and density fluctuation terms. D ( r ) is now proportional to the number of pairs of scattering lengths separated by the distance r in the volume elements p and q, where each value of r is weighted by the product f p - f q . Depending on the solvent scattering density, some volume elements can make a negative contribution to D ( r ) . As previously, the contrast dependence of D ( r ) is readily derived in terms of three basic functions: D ( r ) = AP2DVW + APDv,(r) + D F ( T )

D v ( r ) results from the self-convolution of the shape function and is thus always positive. DvF(r) and D F ( r )result from the convolution of the shape and fluctuation functions and the self-convolution of the fluctuation function, respectively. Both these can be positive or negative depending on the distribution of densities within the particle. The calculation of D ( r ) for simple models is straightforward where analyical expressions are available, such as for full and hollow spheres, and thin circular discs. For a uniform sphere of diameter D:

For an assembly of n spheres of radius R , D ( r ) can be derived by Fourier transformation of the I(Q ) calculated from the Debye method of spheres. Alternatively D(r ) can be calculated directly: N

D ( r )=

N-1

N

c P m r N +2 c c

fl=l

P,P,D(r,dn,,R)

n=l m=n+l

D ( r ,R ) is the distance distribution functiofi of a sphere of radius R , and D(r,d,,,, R ) is the cross-term distance distribution between the nth and mth sphere with a mutual distance d n m .

3. Experimental practice and instrumentation 3. I . Sample preparation and measurement

A good solution scattering curve is dependent on careful sample preparation, satisfactory biochemical and physical assays, accurate background subtractions, a suitable sample holder and instrumental calibration. Aspects of these five topics are briefly noted.

183

3. 1.1. Sample monodispersity and concentrations

In X-ray and neutron scattering, the biochemical requirements for samples must satisfy criteria of monodispersity as well as the usual one of adequate purity. Monodispersity effectively means that the solution is free from non-specific aggregates of comparable sizes to that of the particle of interest. This can be tested prior to experiment by photon correlation spectroscopy or by ultracentrifugation, and in the scattering experiment by a linear Guinier plot at low Q which gives a correct M , (Section 2.6). If required, gel filtration will remove aggregates. Monodispersity also means the absence of degraded material formed by accidental protease or nuclease activity. Sample concentrations in the range 1 - 10 mg/ml are usually sufficiently dilute that no correlations due to interparticle interference effects will occur. These would be evident from reduced I ( Q ) values at low Q in Guinier plots or a negative trough near Dmaxin D ( r ) plots. Qualitatively, the distance between particles, which is given by ( M , / c . N,)'/3, should be larger than 2v/Q. When Q . D,, > 5 (depending on the system), interference effects become negligible and higher concentrations can be used. At higher concentrations, it is then necessary to allow for changes in sample transmissions relative to buffer, and the volume fraction occupied by the solute in the solution. In general, I ( Q ) should be measured at 3-5 sample concentrations c in a dilution series below 10 mg/ml to avoid these complications. The R , and Z(O)/c values should be plotted as a function of c to confirm the absence of concentration-dependent phenomena and the reproducibility of the measurements. Since higher starting concentrations ( - 30 mg/ml) are required for conventional anode X-ray sources or medium-flux neutron reactors, dilution series on such instruments are more important.

-

3.1.2. Sample assays The most important biochemical assay is that for sample concentrations. This is required for absolute M , calculations from X-ray and neutron Z(O)/c values, for neutron matchpoint determinations, and for accurate curve scaling if different Q ranges of I( Q) have been measured. Accurate spectrophotometers and absorption coefficients are needed. For proteins and glycoproteins, A 280, the absorption coefficient, can be calculated from sequence data if biochemical determinations are not available [37]. Biochemical activity and sodium dodecyl sulphate-polyacrylamide gel electrophoresis assays are essential controls before and after the scattering experiment in order to verify sample integrities. In X-ray scattering the sample will absorb X-rays and can suffer radiation damage during exposure. Absorption in the case of neutrons is usually negligible and the beam losses that occur are primarily due to incoherent scattering over 47r. Samples are not therefore degraded by neutron beams. After monodispersity tests, the most important physical assay is that of the sample and buffer transmission measurement. These are required for accurate sample-buffer subtractions (below) and for M , and matchpoint determinations (Section 2.5). Since the neutron transmissions of H,O and 'H,O range from about

184

0.4 to 0.9, transmission measurements will also give the volume ratio of H 2 0 :'H20 in the buffer and hence the solvent density ps can be calculated. In practice, H,O : 'H,O ratios are best determined by careful mixing and dialysis, and transmissions are subsequently used to verify the preparations. For X-rays, ps is determined from knowledge of the buffer composition, correcting for non-ideal mixtures (of NaC1, NaBr, sucrose) using standard tabulations of the concentrative properties of aqueous solutions (Table 2). High salt concentrations diminish X-ray sample transmissions, and light ions such as Li+ or F- should be preferred to heavy ones such as K+ or C1-. Contrast variation by H,0-'H20 mixtures involve almost no structural perturbation of the macromolecule beyond possible 'H--'H exchange and hydrogen bond effects. Corrections for isotope effects on pH measurements are not required. While the Glasoe-Long correction p2H = pH + 0.4 can be used, in practice this has no effect since both the pH electrode and the pK value of ionisable groups are similarly affected, as shown from proton NMR studies of single residues [1-31. Contrast variation by the addition of salt or sucrose can cause structural changes or severe disruptions in macromolecular systems, and the absence of such structural artefacts should be demonstrated in the course of data analysis. Partial specific volume ij measurements are required also (Section 2.3). 3.1.3. Sample backgrounds Scattering experiments measure the total scattering from the sample cell and the buffer as well as that from the sample itself. The cell and buffer contributions have to be subtracted in order to leave the scattering curve of the particle (Fig. 9). Measurement of a buffer blank must therefore be made under identical conditions to that of the sample. Dialysis of the sample solution against its buffer and use of the dialysate buffer are thus essential precautions. With X-rays, since the materials of the cell windows can absorb a large fraction of X-rays, the same cell should be used for the sample and blank runs in order to equalize the scattering of the cell in both runs. With neutrons, the use of quartz ultraviolet spectrophotometer cells of the same type is sufficient. Temperature control is important for buffer subtractions in both X-rays and neutron experiments, in particular for the cases of wide-angle X-ray or neutron (in 'H,O) curve measurements or Guinier neutron measurements in H,O buffers where sample scattering intensities relative to the background are reduced.

3. I . 4. Sample holders The thickness of sample cell holders is optimally given by the reciprocal of the absorption coefficient. While the scattered intensity increases linearly with thckness, the sample absorption, however, increases exponentially. The scattered intensity reaches its maximum value when the incident beam is weakened to l/e = 0.37, and this means that 1 mm thick samples are usual in X-ray and neutron work in H 2 0 buffers. For neutron work in ,H,O buffers, 2 mm thick samples are usual, even though the optimal thickness is now greater than 10 mm. Samples that are too thck may lead to curve artefacts from multiple scattering events. Allowance for

185

Channel number

Fig. 9. Display of typical raw measurements collected during solution scattering experiments using synchrotron X-ray radiation on Station 7.3 at Daresbury in June 1984. (a) Raw scattering data for a sample of a, acid glycoprotein (10 mg/ml): (b) its buffer (0.23 M MgCl,, 0.05 M Tris-HC1, pH 8.3); and (c) the detector response. Note the rise of the intensities close to the beam centre, which is attributed to background scattering. (d-f) Spectra recorded for calibration of the linear position-sensitive detector used in X-ray scattering, i.e. (d) a specimen of wet, stretched rat-tail collagen (spacing 67 nm, with the orders numbered); (e) a specimen of dry, white adductor muscle from the clam Mercenaria rnercenaria (spacing 14.4 nm); and ( f ) the beam centre measured after attenuation of the primary beam.

beam absorption due to the cell itself is required in order not to underestimate the optimum thickness. The cell windows canfbe glass, quartz or mica for X-rays and should not absorb or scatter X-rays too strongly. Thus thin mica platelets of 10-15 pm thickness held in a Teflon support or 1 mm diameter quartz capillary tubes can be used. Air bubble formation in the X-ray cell is a frequent problem which is not easily avoided; sample degassing by warming to ambient temperatures or by evacuation can be of use. Mica windows sometimes absorb visible deposits from the sample in the course of synchrotron X-ray irradiation and these may require changing in the course of the experiment. 3.1.5. Instrumental calibration

Instrumental calibration procedures are required to define the parameters used in scattering curve calculations. The use of position-sensitive linear and area detectors have enormously increased the rates of data collection. Detector responses have to

186

be measured in order to allow for the varying efficiencies of individual elements within these detectors. In X-ray scattering, a uniform radioactive source is employed (Fig. 9). In neutron scattering, the incoherent scattering of a 1 mm thick water sample is used after subtracting the scattering of the empty cell in its holder. If the spatial disposition of detector elements is not known from the linear dimensions of the camera, as in X-ray scattering, wet stretched rat-tail collagen (Bragg spacing 67 nm) or dry white adductor muscle (Bragg spacing 14.4 nm) can be used (Fig. 9). The collagen d-spacing of 67 nm is, however, sensitive to the hydration of this standard; it is reduced to values of 63-65 nm on drying. The position of the beam centre is determined by measuring the strongly-attenuated main beam after removal of the beamstop (Fig. 9), or from the profile of scattering about the beamstop. For neutrons, this profile has to be accentuated by use of a 1-2 mm thick Teflon sample. Background radiation and electronic noise in neutron scattering is measured using a 1-2 mm thick cadmium sample to absorb and remove the main beam. 3.2. Labelling techniques and deuteration Macromolecular labelling in X-ray scattering necessitates the use of covalently-bound heavy metals which are prepared by chemical means. In neutron scattering, labelling involves the selective replacement of 'H by 'H at non-exchangeable CH sites, and is becoming more widespread in its applications. Lipids and detergents can be deuterated by chemical means. Proteins, nucleic acids and carbohydrates are more easily deuterated in vivo by a variety of cell culture methods. Media containing 99.8% 'H,O are capable of supporting microalgae, bacteria, cyanobacteria, yeast and moulds. Media containing maximally 40-80% 'H,O will support liverwort, higher plants, tissue cultures and protozoans, while mammals are able to survive on 15-30% 'H,O media but are not able to reproduce. Thus the incorporation of 'H into macromolecules from the solvent can readily proceed in the cases of algae and bacteria. The use of protonated carbon sources such as glycerol, glucose or succinate in the growth medium is cheaper than the use of deuterated acetic acid or glucose. This leaves bulk ' H 2 0 purchases as the major expense of deuteration. For mammalian macromolecules, tissue culture methods can be employed using protonated solvents to which deuterated substrates obtained from hydrolysates of fully-deuterated algae or bacteria can be added as carbon source. However, the advent of modern genetic engineering techniques should permit the production in bacteria or yeast of the mammalian macromolecules that are otherwise hard to deuterate. Deuteration levels are dependent on the protonated carbon source in use for reason of the exact relationship that the carbon source has to the metabolic pathways in operation. Deuteration levels are best assayed by NMR methods [l-31, both in vivo and in vitro, and checked in the neutron experiment by a matchpoint determination [61]. For example, Escherichia coli grown in 100%*H,O with glycerol will lead to 60% deuteration of RNA and 90% deuteration of protein. Of great practicality is the use of RNA and proteins which are deuterated to match out in exactly 100%'H,O. This can be done with E. coli grown on a glucose source in 76% 'H,O for RNA and 84% 'H,O for proteins. Ribosomes prepared from these are

187

more homogeneous in neutron scattering densities than fully protonated ones [62]. Other deuteration methods for the proteins of E. coli are noted in Section 4.3.1. 3.3. Sources of X-rays and neutrons

X-ray beams can be generated by anode or synchrotron sources, while neutron beams are obtained from nuclear processes using either an atomic reactor or by spallation processes. 3.3.I . Anode sources X-ray beams can be generated from anode sources [4,7], since X-rays are produced when a beam of high energy electrons in a vacuum strikes an anode target, usually copper, whereupon part of the energy of the electrons is converted into X-rays and the rest into heat. The voltage at which the X-ray tube is run will affect the wavelength range of the X-ray spectrum and its intensity. For Cu K , radiation ( A = 0.154 nm), an excitation voltage of 40 kV is frequently used. To monochromate the X-ray beam, the Cu K p radiation ( A = 0.139 nm) can be removed by a thin nickel filter, and this is often used with an electronic pulse height discriminator in the detection system to eliminate photons of greater or lower energies than the K , photons. Crystal monochromators have also been used, which are able to yield the K,, component free from the Ka2 component of Cu radiation. Greater X-ray intensities (3 - 30 times larger than sealed tubes) can be achieved by rotating the anode to diminish target heating, even though this involves moving parts within a high vacuum system which can present maintenance problems. 3.3.2. Synchrotron radiation Even higher X-ray intensities (between 10 - lo7 times more intense than anode sources) can be realized with a synchrotron source [5,14,63]. Initially synchrotron radiation was produced as a by-product in particle accelerators designed for high energy physics research, and was initially available in this way on a parasitic basis (e.g. DESY in Hamburg). Since then dedicated synchrotron sources, starting with the SRS at Daresbury, have been constructed for producing synchrotron radiation (Fig. 10). For solution scattering, the special properties of a synchrotron source for scattering work are (a) very high intensity; (b) very good intrinsic collimation; (c) the source is white. Others are (d) the radiation is plane-polarized; (e) the radiation is emitted in pulses. In a synchrotron or a storage ring, the electrons (or positrons at LURE, Orsay) travelling at a very high speed are constrained in a circular trajectory by means of electromagnets. The electrons are subjected to a strong centipetal acceleration in each bending magnet. Accelerated charges radiate energy including X-rays, and this lost energy is replenished by an oscillating radiofrequency electric field. The total radiated power P is: P

= 88.47E 41R-

where E is the acceleration energy (GeV), I is the current (amperes) and the orbital

188

TO BIOLOGY CHEMISTRY 8 PHYSICS LABORATORIES

FROM CONTROL

P . b

ROOM CORE

SCATTERING INSTRUMENT D17

R EACTOR B U I L D I N G

“IDE

HALL

DATA COLLECTION CABINS

SCATTERIN ^

\

NEUTRON GUIDES

Fig. 10. Schematic layout diagrams of high-flux X-ray and neutron sources. (a) Top view of the 2.0 GeV SRS synchrotron at Daresbury. The linear accelerator (bottom left) feeds electrons to the booster synchrotron (bottom right) which injects these in a total of 160 bunches to fill the main storage ring. The current lifetime (200-400 mA) is about 8 hours. Synchrotron radiation is emitted by the high energy electrons as they orbit the storage ring inside its vacuum vessels, and ports at points around the circumference of the ring allow beams of radiation to be taken to the experimental stations. (b) Top view of the high-flux neutron reactor (which operates at 57 MW) and guide hall at the Institut Laue-Langevin in Grenoble. The fuel element contains 9 kg of uranium enriched to 93% by U235and has an operating cycle of 44 days. Reactor cooling and neutron moderation are effected by heavy water circulation passing through heat exchangers. Neutron beams are available from ports in the reactor hall and neutron guides

189 C

i o n and shielding Synchrotron 3

Linac 70 MeV H-10

Ion source and preinjector 665 k e v H-ions

in the guide hall. For solution scattering, a cold source of 25 dm3 of liquid deuterium at 25 K enhances the intensity of neutrons at long wavelengths. (c) Perspective view of the spallation neutron source at ISIS at the Rutherford-Appleton Laboratory to show the 800 MeV synchrotron (200 p A mean current) which delivers a 0.4 psec proton pulse at 50 Hz onto a depleted uranium target. The target is cooled using heavy water, and is surrounded by a 4.3 m thickness of steel and concrete. There are 18 ports through which neutrons pass to the instruments, either directly or through neutron guides.

radius is R (metres). The critical wavelength A, wavelength cutoff of the spectrum and is given by:

A,

is approximately the short

= 0.559RE-3 = 1.864B-lEP2(nm)

where B is the magnetic field (Tesla). The intensity near its maximum strength (which varies as a function of wavelength) is given by 17 X 10-21E7R-3.The white X-ray beam of photons must be monochromatized and brought to a focus in the camera. This is best achieved with a highly-polished curved mirror, which is used at grazing incidence to the beam and set at right angles to a curved crystal monochromator, typically a Ge or Si perfect single crystal. This leads to vertical and horizontal focussing. Together with the use of position-sensitive detectors in place of proportional counters, the use of synchrotron radiation has shortened exposure times by a factor larger than lo5. The principal drawbacks of synchrotrons are the problems of continuous routine operation resulting from (a) the complexity of instrumentation, some of it still under development, and (b) the finite decay of the electron beam with a half-life of several hours once injected into the ring, which necessitates beam dumps and reinjections, and the planning of experiments around these dumps. 3.3.3. Reactor neutron sources Neutrons for scattering have wavelengths of the order of 0.1 - 1 nm and are generated by the use of medium-flux (10 - 20 megawatts) or high-flux (60 - 100

190

megawatts) nuclear reactors [36,64,65]. The fission of U235in a specially-designed reactor core produces fast high-energy neutrons (Fig. lo), which pass from the core into a moderator such as 2 H 2 0 or graphite at 300°K to lose energy through collision until they reach thermal equilibrium (A,,, 0.1 nm in the Maxwellian distribution). Further moderation using a cold source such as liquid deuterium at 25 OK further enhances the longer wavelengths (Apeak 0.5 nm) that are useful for solution scattering. The longer wavelengths relaxes angular resolution restrictions in the neutron camera. Neutron guides deliver the neutrons from the reactor to externally-located instruments. The first section of the guide is bent to eliminate y rays and fast neutrons. A velocity selector based on a rotating drum with a helical slit in it monochromates the Maxwellian while minimising flux losses by permitting only neutrons with a specific velocity range ( = wavelength) to be transmitted. Monochromatization can be alternatively achieved using the reflection planes of pyrolytic graphite crystals.

-

-

3.3.4. Spallation neutron sources Spallation neutron sources use proton accelerators to generate neutrons [66]. The proton beam is accelerated through 500-800 MeV to strike a target made of uranium or tungsten (Fig. 10). Each proton dislodges about 10-50 neutrons from the nucleus it hts, hence the term “spallation . Since the heat generated in the target can be dissipated between the pulses, pulsed sources have a potential for significant increases in flux over reactor sources, where the removal of the intense heat in the core is a limiting design factor. Neutrons are produced at very high intensities in 1-50 psec pulses spaced 20-100 msec apart. Time-of-flight techniques based on the time required for a neutron to reach the detector after scattering from the sample permits the efficient usage of all the neutrons in each “white” pulse, and simultaneously achieves monochromatization of the beam. Spallation sources thus lead to different instrumental approaches, although cold sources are again used as for reactor sources to increase the neutron wavelength. A further relevant property of pulsed sources in distinction to reactors is the production of high fluxes of epithermal neutrons whose kinetic energy is just above thermal energies. 3.4. Scattering instrumentation 3.4.1. X-ray cameras Cameras collimate and direct the primary beam to the sample, and subsequently record the scattered intensities. Scattering theory has been derived for a point source. For conventional X-ray anode sources, the beam intensities are too weak to be employed in this way, and slit sources have been employed in place of pinhole sources. These produce a beam of narrow rectangular cross-section. Slit (or line) sources can be considered as a linear arrangement of a large number of point (or spot) sources. The resulting scattering curves are convoluted by slit-smearing effects. Thus experimental curves have to be mathematically desmeared, in particular at low Q in the Guinier range, and t h s process can be complex. In the Beeman camera, the simplest collimation consists of two pairs of parallel

191

slits, one near the source and one near the sample [67]. The slits will, however, introduce secondary (or parasitic) scattering into the small angle region at low Q; a third pair of slits after the second pair can reduce this. An additional two pairs of slits after the sample define the scattering angle 28 and reduce parasitic scatter in the proportional counter. The Kratky block camera is very successful in eliminating parasitic radiation from slits and so offers improved curve resolution [67]. The initial pairs of slits before the sample are replaced by a precisely machined asymmetric system of steel blocks to produce a region free of parasitic scatter very close to one side of the direct beam. The prices to be paid are (a) the inaccessibility of the scattering curve on the other side of the direct beam, thus requiring an indirect determination of the beam centre, and (b) some screening of the wide-angle curve. Scattering curves are measured using a proportional counter which is automatically stepped to scan 28, although linear detectors are now finding application in Kratky cameras. Synchrotron radiation X-ray instruments are characterized primarily by reason of their high direct beam intensity [68,69]. Point collimation can now be used in place of slit collimation, so avoiding the need for curve desmearing (Fig. 11).Two round apertures can be used, where the first defines the beam and the second limits parasitic scatter. In practice, pairs of horizontal and vertical slits are placed before and after the crystal monochromator, and before the mirror and the specimen. Cameras can be made longer with movable detector positions to improve the accessible Q range. However, the high background radiation levels make it impossible to work near the instrument in the presence of the beam. Camera alignments and its operation must be done by remote control. Four kinds of detectors have been used: (a) X-ray film; (b) television detectors; (c) linear position-sensitive detectors; (d) multi-wire area detectors [70]. Detectors have typically 250 - 1000 resolution elements along an axis. One drawback of (c) and (d) is the need to avoid saturation count rates from strongly scattering samples. For spectral normalisation, beam monitors employ an ion-chamber for the integration of main beam intensities during data collection. 3.4.2. Neutron cameras Neutron cameras on reactor and spallation sources require careful optimal design for reason of the relatively low neutron fluxes and scattering cross-sections (Fig. 11) [64]. In addition to the use of long neutron wavelengths, additional characteristics involve the use of (a) wide neutron beams of cross-sectional area > 1 cm2; (b) samples of large surface areas 1 cm2 incident to the main beam; (c) two-dimensional area detectors of dimensions 64 X 64 cm2 with 1cm2 elements. The large beam sizes can lead to beam divergence errors, and the collimation distance is varied by the use of movable segments of neutron guides to optimize the desired point collimation. The incident and scattered flight paths should be set equal for optimal resolution. The beam area incident on the sample is adjustable using two pairs of vertical and horizontal slits or circular diaphragms. The detector assembly is positioned in vacuo in a large tube, and ranges of sample-detector distances of 1- 40 metres are possible. Neutrons are detected with BF, gas in an ionization chamber. BF, is

192 E l e c t r o n beam

Curved crystal

X - r a y beam

Sample

Detector

> m\&?bdp$ Collimation

6 4 x 6 4 area Multldetector

DATA HANDL.ING

NEUTRONS

Velocity Selector

I

;

Diaphragm!

I I

!

+2-40m1-2-40m

-i

Fig. 11. Schematic diagrams showing the construction of small angle scattering instruments. Upper: The optical system used at Station 7.3 at the SRS, Daresbury. In addition to the system as shown, there are horizontal and vertical slits before and after the Ge(ll1) curved-crystal monochromator (used for horizontal focusing as well), and before the specimen. Slits before the platinum-coated mirror (used for vertical focusing) are used to prevent radiation hitting the ends and the mounting of the mirror. Data are recorded with a multi-wire area detector or a single-wire linear detector, which is interfaced with a local minicomputer for data collection and storage. Lower: The layout of the neutron camera D11 at the Institut Laue-Langevin in Grenoble. A helical velocity selector is used for monochromatisation (9% full-width-half-height). Movable neutron guides give collimation distances of 2, 5, 10, 20, and 40 m. The beam size at the sample is defined by an adjustable diaphragm. The 64 X 64 element BF, multidetector is contained within a 40 m evacuated tunnel, and can be moved on a trolley by remote control in a range of sample-detector positions between 2 to 38 m in the direction of the primary beam. The detector is interfaced with a local minicomputer system for data collection and storage.

mainly used for subthermal neutrons; 3He is useful for thermal neutrons. The detector is interfaced to a minicomputer system that provides data accumulation control, main beam monitoring, storage and data reduction. In a spallation source camera, adaptations are required to allow for the high flux of faster neutrons and the pulsed nature of the source [71,72]. Fast neutrons of wavelengths <0.1 nm are deflected out of the beam prior to final collimation by the use of Soller supermirror benders. Wavelength selection choppers control the neutron wavelength distribution within each pulse, and prevent frame overlapping between consecutive pulses. High detector count rates are achieved by the use of 6Li-glass scintillation elements connected to photomultiplier tubes, although helium detectors can be used. Each neutron pulse is analysed as 64 time-channels, each one of which corresponds to a 64 X 64 two-dimensional scattering pattern with its own

193

wavelength. The time channels are subsequently merged in data reduction; the computational requirements are therefore considerably larger than for reactor source cameras. 3.5. Data reduction

X-ray scattering curves (see Fig. 9) are extracted by simple subtraction of the sample and buffer curves, and in the cases of linear or area detectors are normalized for detector responses by:

Neutron curves are calculated similarly [73], although account of the cadmium and empty cell backgrounds is required. Icadmium(Q)is first subtracted from the four curves in question, and '((2) is obtained from:

Three types of instrumental errors on ' ( Q ) can require attention, namely (a) the collimation (including both beam divergence and slit smearing); (b) wavelength spread; (c) the finite size and depth of detector elements. In X-ray scattering, slit-smearing can be corrected by breaking t h s down into two one-dimensional effects for each of the slit length and width, and calculating the convolution integrals; curves are primarily affected at low Q [58]. There is an extensive literature on desmearing corrections, which involve corrections of either the experimental curve or a modelled curve. Wavelength spread and detector depth effects are zero at zero Q and increase linearly with 20. Thus in neutron scattering and synchrotron X-ray scattering with point (or spot) sources, scattering curves at small Q are not distorted. At larger Q, since the halfwidth of the wavelength distribution is about lo%, neutron curves are significantly affected by ths, and also by beam divergence if wide beams are in use. Detector errors are usually neglected, especially for large sample-detector distances. The general effect of smearing on scattering curves is to smoothen the maxima and minima as seen in Fig. 7, and to decrease the rate of decrease in I(Q) as Q increases.

194

Part B: Biochemical Applications to Proteins, Carbohydrates, Lipids and Nucleic Acids

4. Applications of X-ray and neutron scattering 4.1. Introduction

Many solution scattering studies have been based on globular proteins and metalloproteins using X-rays, since these can readily be analysed as monodisperse systems [12,74]. Extensive applications have been described in the literature. Neutron scattering on proteins and metalloproteins provides complementary additional information on internal structures, solvation shells and the internal topology of subunits in multimeric structures, and are considered separately below. Glycoprotein studies bear many methodological resemblances to those on proteins and metalloproteins. However, for reason of the possibility to analyse the carbohydrate component as a distinct entity, glycoproteins are discussed separately below. The study of membrane and nucleic acid systems presents greater complexities. The study of lipids and insoluble membrane proteins in association with them can be achieved in solution scattering [75,76] by the use of lipid vesicles to solubilize the system of interest. Membrane proteins can alternatively be studied by solubilization using detergent micelles. The exception to this generalization is the group of plasma lipoproteins which are readily soluble in aqueous buffers. Systems with nucleic acids (i.e. protein-nucleic acid complexes, viruses, ribosomes and chromatin) [24-27,77,78] are not affected by these solubility problems. However, lipid and nucleic acid systems are both further complicated in their analyses by the polyionic character of these macromolecules. Particular care is required concerning the partial specific volumes of the individual components to be used within the system of interest. 4.2. X-ray studies on globular proteins 4.2.1. Relationship between R , and M, X-ray solution scattering has been applied to the small proteins whose crystal structures were among the earliest to be determined (myoglobin, lysozyme, ribonuclease, chymotrypsin, cytochrome c). Its application often predated the crystal structures. With the solution of these crystal structures, further studies subsequently employed these as useful model systems for scattering work [lo-121. Since then, X-ray studies have been applied to proteins of increasingly larger M , with known or unknown crystal structures. A literature survey of R , values is summarized in Fig. 12 where values of log R , are plotted against log M , for 53 globular proteins. For a spherical protein ( U = 0.74 ml/g), R , is related to M , by:

log R ,

= 0.333

log M, - 1.289

195

I

10000

I

I

I

I

50000

1

1

1

I

,

I00000

I

I

,

I

, , I (

500000 1000000

Mr

Fig. 12. Relationship between R, and M , for globular proteins. Literature data are presented for the following 47 proteins in order of increasing M,: parvalbumin, cytochrome c, ribonuclease, a-lactalbumin, lysozyme, myoglobin, DD-carboxypeptidase, a-chymotrypsin, tryptophan synthase (a),riboflavin binding protein, L-arabinose binding protein, pepsin, P-lactoglobulin, a-lactoglobulin, arginine kinase, cytochrome P-450,hexokinase, inorganic pyrophosphatase, haemoglobin, bovine serum albumin, malate dehydrogenase, tryptophan synthase (P2), aspartate aminotransferase, tubulin subunit, hexokinase (dimer), ATPase Fl ( a2),myosin S1, tryptophan synthase ( a2P2),glyceraldehyde-3-phosphatedehydrogenase, P-lactoglobulin (octamer), malate synthase, pyruvate kinase, catalase, 11s globulin (rape), 11s globulin (sunflower), aspartate transcarbamylase, glutamate dehydrogenase, 11s globulin (soyabean), phosphofructolunase (D-saline), 11s globulin (field bean), 11s globulin (pea), adenosine triphosphatase, ribulose bisphosphate c.arboxylase, phosphofructokinase (yeast), haemocyanin (A. leptoducrylur) haemocyanin (C. pugurn), haemocyanin (H. vulgaris). Where more than one R , value is known for the protein or its ligated derivative, the range of the observed R , values is shown as a vertical line. The six R, values for DNA-dependent RNA polymerase and its subunits are shown as open circles (see text).

or Ro = 0.051466M,"3

This represents the physically minimum allowable RG for a protein. Fig. 12 shows that all the proteins studied so far are significantly more elongated than spheres, and that this difference is for the most part steady in a M, range between 104-106. With the exclusion of the six RG values for DNA-dependent RNA polymerase and its subunits (see below), a regression analysis for the R G values of the remaining 47 proteins gave a correlation coefficient of 0.991 and the line: log R ,

= 0.365

log M , - 1.342

The slope of the line of 0.365 is close to the value of 0.333 which is anticipated from

196

the expression in Ro above. The mean value of RG/Ro (Section 2.6) for the 47 proteins is 1.28k0.10. Fig. 12 shows a tendency for proteins to become more elongated with increase in MI, although the RG values exhibit more scatter at h g h M,. Thus from the regression, RG/Ro is 1.18 for M , = l o 4 and RG/Ro is 1.37 for M, = lo6. DNA-dependent RNA polymerase is an interesting exception which is related to its biological assembly. This has a 4-5 subunit structure which was investigated in 6 different forms termed a 2 , u, pa,, p)Pa2, /3‘/3a2u and (p’/3a2u>, in order of increasing MI. The R , for the smallest subunits are substantially larger than expected from their MI. On formation of the 4-5 subunit core enzyme and the holoenzyme and its dimer, the RG values approach the regression line of Fig. 12. 4.2.2. Comparison of crystal and solution structures The earliest studies were directed towards the corroboration of protein crystallography results. In some cases larger RG values were observed. Thus myoglobin initially had an RG of 1.8 nm in distinction to the crystallographic RG of 1.55 nm. This discrepancy was resolved by the use of gel-filtration to separate monomeric myoglobin from the presence of more than 5% dimers and some higher aggregates [12]. Lysozyme and a-lactalbumin are structurally closely homologous proteins; however, they originally exhibited different RG values of 1.43 and 1.67 nm, respectively [12]. Subsequent R , determinations for a-lactalbumin have given an R , of 1.45 nm [ll], in better agreement with that for lysozyme and its crystallographic RG of 1.38 nm. Other investigations have compared the large angle scattering curve (2 nm-’ < Q < 7 nm-’) with crystal structures at 0.6 nm resolution. These simulations require an accurate description of the way in which the solvent density p s and the protein hydration shell affects Z(Q). I ( Q ) in turn will be affected by the experimental difficulties in measuring low intensities at large Q. Discrepancies between the calculated and measured curves were investigated by modifying the crystal structure according to physical and functional considerations, e.g. 5 O - 1 0 O peptide chain rotations or shfts. For myoglobin two minor modifications of the crystal structure were proposed, although it was not possible to choose between them [79,80]. For phage T4 lysozyme, differences were found which were ascribed to movement of the polysaccharide-binding cleft [81]. Ribonuclease data out to Q = 5 nm-’ were, however, found to be the same in the crystal and in solution [82]. 4.2.3. Conformational changes and Iigand binding Ligand binding in certain proteins can be usefully followed by X-ray scattering, where conformational changes are reflected in intensity changes seen in the scattering experiment. The relative magnitudes of such RG changes compared to the RG value are shown in Fig. 12. The conversion of chymotrypsinogen into a-chymotrypsin by peptide bond cleavage leaves the respective RG values of 1.81 and 1.80 nm almost unchanged, in accordance with crystallographic results [831. The binding of pyridoxal 5’-phosphate to aspartate aminotransferase causes no change in the RG value of 2.90 nm [84], also in agreement with results from crystallography, even

197

though conformational differences in the free and ligated forms have been identified by physical techniques such as fluorescence and H-2H exchange. This discrepancy is attributed to the local and minor nature of these conformational changes. In many other systems, distinct RG changes are observed. The binding of substrates or substrate analogues to malate synthase causes the R G of 3.96 nm in the free enzyme to decrease by 0.03-0.06 nm [85-871. The RG of 2.115 nm for arginine kinase decreased by 0.120 nm upon binding ADP-Mg2+ and L-arginine, ADP-Mg2+ alone or ATP-Mg2+ alone [88]. The active and inactive forms of ribulose bisphosphate carboxylase (which are interconverted by variation of the concentration of HCO; and Mg2+) have RG values of 4.78 and 4.92 nm, respectively. The binding of riboflavin to the riboflavin-binding protein (a transport protein in egg-white) was studied as a function of pH [90]. At pH 7 the indoprotein has a RG value of 1.98 nm, while at pH 3.7 the apoprotein has a RG of 2.06 nm corresponding to the release of riboflavin and formation of a more extended shape. Control sedimentation experiments in fact showed identical s& values for the apo- and holo-forms at pH 7, indicating that riboflavin binding has no influence on the protein tertiary structure at pH 7. Studies on the soluble portion of the adenosine triphosphatase membrane complex involved in oxidative phosphorylation and photophosphorylation showed that on ligation with ADP the RG value decreased from 4.95 to 4.78 nm [91]. Since small RG changes can be involved, particular care is required during measurements, and supportive data from other measurements are desirable [90]. In summary, substrate binding to proteins have usually led to decreased RG values where RG changes have been detected, and these correspond to more compact ligated protein structures. Calmodulin is an exception, where Ca2+ binding causes its RG to increase from 2.06 to 2.15 nm [92]. If crystal structures are available to constrain analyses, solution scattering can lead to well-defined analyses of ligand binding. In suitable cases, it can avoid the need to solve a further crystal structure. As shown in Fig. 13, the binding of glucose and glucose-6-phosphate to hexokinase resulted in a 0.095-0.125 nm decrease in the R , of 2.473 nm for the free enzyme [93]. This decrease is well matched by R , calculations based on the atomic coordinates of native hexokinase and of a glucose complex, and corresponds to the closing of a cleft between two lobes in hexokinase by a 12" rotation of one lobe relative to the other on the binding of substrate (Fig. 13). Further work on hexokinase compared the RG value of the dimeric form with those calculated for two crystal forms of hexokinase where the orientation of the two monomers in the asymmetric unit were substantially different [94]. One dimer structure was ruled out, while the other was compatible with the measured RG value. Note that t h s does not prove that this second structure is the actual dimer structure in solution. In the case of L-arabinose binding protein, the RG of 2.12 nm is decreased by 0.09 nm on the binding of L-arabinose [95]. The crystal structure consists of two similar globular domains. Simulations in which the one was rotated relative to the other about a hinge showed that a 0.1 nm decrease in RG could be obtained by a rotation of 18" f 4". The RG of phosphoglycerate kinase decreased by 0.109 nm when it bound ATP-Mg2+ and 3-phosphoglycerate [96]. The crystal structure exhibits two lobes with a substrate binding cleft between them; computer-

198 I

I

1

I

Hexokinase concentration ( r n g / r n l )

Fig. 13. Upper: Summary of the R , measurements for native hexokinase (M) and in the presence of glucose (A) and glucose-6-phosphate (0).The concentration dependence of the R , values was taken from the best R , data set for the native enzyme. The values extrapolated to zero concentration are 2.473, 2.378, and 2.348 nm in that order, with errors of k0.02 nm. Lower: A drawing is shown of the projected outline of the actual crystal structures of unligated hexokinase (left) and hexokinase-glucose (right). In the absence of glucose (G), the enzyme has an open structure with a deep slit, while in the presence of glucose the conformation changes to give a closed structure [93].

simulated cleft closure showed that a 8-14" rotation of one lobe relative to the other could reproduce the experimental RG change. 4.2.4. Allostericism Solution scattering can be applied to study allostericism in multisubunit proteins. The classic example is haemoglobin. X-ray and neutron scattering have both detected a decrease of 0.05-0.15 nm in the RG of deoxyhaemoglobin when t h s binds oxygen [97-991. Calculation based on the two crystal structures revealed a 0.035 nm change in the R G values, thus corroborating the solution results. Since the maximum atomic movement within haemoglobin is 0.6 nm, this provides some idea of the magnitude of conformational change that is detectable by solution scattering. Glyceraldehyde 3-phosphate dehydrogenase, an enzyme of oxidative phosphorylation, is a four-subunit enzyme which binds up to four NAD molecules. Titration experiments with NAD showed changes in the values of the RG and the volume that were not linear as a function of NAD concentration [100,101]. This verified the existence of allosteric properties, in good agreement with lunetic measurements, and now rationalized by the determination of the crystal structure. Thus on the full binding of four NAD molecules, the RG decreased by 0.08 nm and the volume by 7%. Phosphofructokinase, a key enzyme in glycolysis, also has allosteric properties, however in this case no conformational changes could be detected in the presence or absence of the substrate fructose 6-phosphate or addition of the activator AMP

199

Q (nm-')

Fig. 14. Complete X-ray scattering curve of aspartate transcarbamylase based on experiments in the two Q ranges of 0.06 - 1.6 nm-' with dilute solutions (4 - 12 mg/ml) and 0.3 - 3.8 nm-' with concentrated solutions (110-120 mg/ml) [104]. U = unligated enzyme; L = ligated enzyme (with PALA: N-phosphonacetyl-L-aspartate) [104].

[102,103]. In the presence of ATP, however, as an inhibitor, the enzyme underwent a non-allosteric conformational change where the R increased and secondary minima and maxima are shfted to lower Q values, which correspond to a more expanded, inhibited structure. Aspartate transcarbamylase (ATCase) from E.coli is a 12-subunit enzyme which undergoes a cooperative activation in the presence of both its substrates, carbamoyl phosphate and aspartate. Its activity is enhanced by ATP and feedback inhibited by CTP. Use of the transition-state analogue PALA (Fig. 14) permits observation of the unligated or ligated forms. Scattering curves out to Q = 3.5 nm-' (Fig. 14) lead to RG values of 4.59 and 4.84 nm for the native and ligated enzyme, respectively, at low Q, and give distance distribution functions with maxima at 5.8 and 6.3 nm [104]. ATCase thus swells in the ligated form and has become more isometric, in consistency with earlier hydrodynamic data and subsequent protein crystallography results. The maxima and minima in the scattering curve can be used to monitor the proportions of the different forms in solution as a function of ATP and CTP concentrations [105]. In summary, conformational changes in allosteric multisubunit proteins do not always lead to decreased RG values in the ligated macromolecule (see previous section). While crystal structures have been used for R , calculations, so far no complete curve simulations have been reported. 4.2.5. Molecular modelling of proteins Molecular modelling strategies based on the use of small spheres have been extensively applied to systems not yet crystallized. The 11s globulins from plant seeds (rape, sunflower, soya, field bean, pea) of M,. 3.0-3.6 X lo5 and the 24s arthropod haemocyanins (crayfish, lobster) of M,. 9 X lo5 are too large to be studied

200

by current protein crystallography methods. Solution scattering has, however, provided molecular parameters to a structural resolution 2 r / Q of 2-4 nm [106-1121. The 11s globulins contain 6 equivalent subunits. The scattering curve in the range of 1 nm-' < Q < 10 nm-' exhibits a number of subsidiary maxima and these, together with the RG of 3.95 nm from Guinier plots and Om,, of 11.0 nm from distance distribution functions D ( r ) , define the particle shape [log]. An ellipsoid of revolution (axes 11 nm x 11 nm x 8.8 nm) fitted the measured curve to Q = 0.9 nm-'. The testing of simple models based on arrangements of 3-12 spheres showed that a trigonal prism and a trigonal antiprism, each composed of 6 spheres in contact, could account for the position of the first subsidiary maximum at Q 1.15 nm-', although not its intensity. Final simulations based on optimising the arrangements of about 1000 small spheres of diameter 1 nm and maintaining the antiprism led to coincidence between the experimental dihedral point group symmetry 32 (D,) and calculated scattering curves out to Q = 1.6 nm-' (including the first two subsidiary maxima) [log]. Data collection has been repeated using synchrotron radiation to show that this has advantages of eliminating the desmearing corrections required with a conventional source and a Kratky camera as well as involving much shorter exposure times and yielding higher angular resolutions [110]. Since the 11s globulins can be dissociated into 2 halves, and into the 6 individual subunits, it should be possible to refine further the trigonal antiprism model using the subunit scattering curves. Other studies have examined a 7 s globulin from P. vulgaris seeds and compared its structure with a crystal structure for a related 7 s globulin [113,1141. Similar procedures have been applied to ,8-haemocyanin from H, pomatia and the 24s haemocyanins from arthropod species [13,74,115-1211. The P-haemocyanin structure ( M , 9 x lo6) was studied intact and also in subunits corresponding to a half, a tenth and a twentieth of the parent structure (Fig. 15). Their RG are 18.4, 13.9, 9.0 and 7.5 nm. The final model for the P-haemocyanin structure is a hollow cylinder built from 160 spheres of radius 2.5 nm; its morphology could be tested by its consistency with data on the subunits and with the experimental curve out to Q = 4.2 nm-' (Fig. 15). The 24s haemocyanins ( M , 9 X lo5) have 12 monomeric units and a R , of 6.9-7.25 nm [74,120,121]. A model composed of two trigonal anti-prisms of 6 spheres each and radius 3.05 nm and joined end-to-end to give a cylinder of length-diameter ratio about 2 : 1 gave good agreement between the measured and calculated scattering curve I ( Q ) out to Q = 2.7 nm-' (including the first two subsidiary maxima) and the distance distribution function D ( r ) [74,120]. Cross-sectional R,, analyses with R,, values of 3.8-3.9 nm confirmed the cylindrical properties of 24s haemocyanins. Molecular modelling using spheres has also been used to study complexes formed from different subunits, i.e. tryptophan synthase ( a 2 P 2 )and its (Y and P2 subunits [122], and likewise the DNA-dependent RNA polymerase (,8'pa,u) and its u, a 2 , Pa2 and Plpa, subunits [123-1271. The tryptophan synthase scattering curves were modelled using spheres of 1.2 nm diameter for each of the (Y and the P2 subunits (total R , of 1.95 and 3.01 nm, respectively). Good I ( Q ) curve fits to Q = 1.3-1.7 nm-' and comparable fits to Q = 4 nm-' were obtained using slightly elongated

-

201

log

a

Fig. 15. Modelling of P-haemocyanin ( H . pornntin) constructed from 160 spheres of radius 2.5 nm with overall dimensions of 39 nm (height) and 34 nm (diameter). For clarity, the 20 subunits at the inner side of the bottom are not drawn. The spheres corresponding to the one-twentieth dissociation product are shown connected by lines to indicate three adjacent units [119]. The comparison between the theoretical (- - - - -) and the experimental () curves is shown. The deviations between the two curves were attributed to limitations in the assumption that the subunits are spherical [119].

ellipsoidal shapes. The structure of the a2P2complex was defined by its R , of 4.01 nm , its R,, and D,, values, and further curve modelling to Q = 2.5 nm-'. It was shown that the complex did not correspond to the close packing of two a subunits and a p2 subunit, i.e. conformational changes had taken place on complex formation. A similar strategy was also applied to the DNA-dependent RNA polymerase subunits, where the R , , R x s , R,,, V and D,, values were measured and used as constraints for modelling the scattering curve using spheres of 1.34 nm diameter [ 123-1251. Since simple triaxial shapes could not replicate the experimental curves, more involved, elongated subunit shapes using a trial-and-error search had to be proposed to fit the measurements. The final model for /3'jla2u is triangular where a 2 constitutes its base, /3 and /3' constitute the two sides, and u is positioned on one face of the triangle [126]. Both the tryptophan synthase and RNA polymerase systems have been further studied using selective deuteration and label triangulation by neutron scattering, in which the X-ray results have been a useful guide of the experimental work (Section 4.3.2). 4.2.6. Associative systems and time-resolved synchrotron radiation studies Scattering studies of associative systems are exemplified by malate synthase, glutamate dehydrogenase and tubulin. Malate synthase undergoes aggregation upon prolonged exposure to X-rays and t h s can be monitored simultaneously by solution scattering [128-1341. The structure of the enzyme can be approximated by an oblate ellipsoid of axes 12.2 nm X 12.2 nm X 4.4 nm [129], and computer modelling was

202

based on this. Experimentally, both the R , and I ( 0 ) increase as a function of irradiation time and beam intensity. Initially a linear row of aggregates is formed, characterized by the R,, value. Subsequent aggregation occurs in a second direction, leading to a second R,, value. The R,, remains unchanged, showing that the aggregates are planar; t h s was verified by computer models based on these rows and on planes [132,133]. Malate synthase is also a useful model for the study of free radical formation, whereupon irradiation by X-ray beams, hydroxide and superoxide radicals together with H202 are formed [134]. Glutamate dehydrogenase also forms elongated aggregates which are in this case dependent on the sample concentration. As the concentration rises, R , and I(0 )increase continuously while the R,, and [ I ( Q ) -Q]p-o values are unchanged [12,135,136]. Calculation of the average length L as a function of M , from I(0 )shows that the association is linear, leading to rod-like particles. This was again verified by computer simulations of the monomer and rod-like aggregates. Synchrotron radiation has enabled time-resolved studies of tubulin assembly and disassembly to be carried out [18,137-1411. Tubulin is a heterodimer of M , 100,000 which tends to form linear arrays of protofilaments. A ring of 13 parallel protofilament rods forms the microtubule wall as a hollow cylinder. Solution scattering was initially used to characterize the structures of stable intermediates, assisted by electron microscopy and X-ray fibre patterns of orientated microtubules (i.e. heterodimers, single rings containing varying numbers of heterodimers, protofilament rods and microtubules). Further analyses showed that the curve intensities at the lowest measured Q values reflect the weight-averaged degree of polymerization (Section 2.6), while at large Q these are independent of the state of aggregation. The proportion of each form present was identifiable since the scattering curves of rings and hollow cylinders exhibit characteristic minima and maxima. Synchrotron X-rays were thus used to record complete curves in intervals as short as every 2-15 sec in order to follow tubulin assembly and disassembly during temperature jumps (Fig. 16). The intermediates could be identified from the scattering analyses, hence enabling the nucleation pathway to be elucidated. Difference spectra were useful to identify the actual intermediates in transition during a jump, since the samples were usually complex mixtures of subpopulations. Thus it was shown that rings disappear prior to microtubule assembly and do not act as nucleation centres as once believed. Instead, the rings break into small fragments of protofilaments which can elongate by the endwise addition of subunits. The nucleation process consists of lateral associations between protofilaments until 13 of them close into a cylinder to form the microtubule. In verification of this scheme, it was shown that chemical conditions such as excess Ca2+ or GDP which stabilize rings act as inhibitors of microtubule assembly. Other time-resolved synchrotron radiation scattering studies have been performed to study the dissociation of aspartate transcarbamylase by mercurials. These showed that a time resolution of the order of 100 msec is possible [142a]. The aggregation of bovine serum albumin after cleavage of its disulphide bonds by reduction with dithiothreitol could be traced in time intervals of 50 sec and also showed that experiments with a time interval of 100 msec are possible [142b].

203

Fig. 16. Projection plot of the scattering traces obtained during two cycles of assembly and disassembly of microtubules in a temperature-jump experiment using synchrotron radiation and a position-sensitive linear detector [138]. Note the changes of I ( Q ) at low Q and also in the subsidiary maxima. At 4"C, rings of tubulin predominate. At 37 " C, microtubules in the form of hollow cylinders predominate in the sample.

4.2.7. Interparticle interference An interesting application of solution scattering is the study of intermolecular organizations of proteins in highly-concentrated solutions. Two examples are 300 mg/ml in human red blood haemoglobin (which occurs at concentrations of 400 cells) [74,143,144] and the crystallins (which occur at concentrations of mg/ml in eye lens) [145]. The use of a concentration-dilution series of Z(Q) curves and calculation of the D(r ) curves identify interparticle interference phenomena, and the data can be compared with calculations of I H S ( Q )using a hard-sphere model (Section 2.9.5) and the determination of the shape of the macromolecule at infinite dilution in the usual way from R,, I ( Q ) and D ( r ) analyses. At high concentration, D(r ) will exhibit positive and negative oscillations with a periodicity close to the diameter of an average molecule. These oscillations are damped at about four diameters for both haemoglobin and the crystallins and are attributed to positional correlations between neighbouring molecules. If the crystallins of the eye lens were independent scatterers, the scattered intensity would be proportional to concentration, and this would lead to the scattering of 70% of incident visible light.

-

-

204

TABLE 9 Summary of X-ray data for proteins analysed by Guinier R , and I ( 0 ) plots and Stuhrmann R, and a plots. These are arranged in order of increasing electron density. Where a matchpoint solution composition is not given, the solute used to vary the solvent contrast is indicated in parentheses Proteins

M,

Experimental electron density ( e .nm-3)

Carbonmonoxyhaemoglobin

64,500 398 3

Oxyhaemoglobin

64,500 403

Bovine serum. albumin Malate dehydrogenase Apoferritin Myoglobin

Adenosine triphosphatase

Chloroplast coupling factor Phosphofructokinase

R , (nm)

a

Ref.

1.56 kO.03

Positive

~501 11501 ~501

(TlBr)

-

Positive

I1541

(sucrose)

5.26

47.5% sucrose (by weight) 76% glycerol (by volume)

68,000 404

6.8 M NaCl

85,000 407 410

7.2 M NaCl 53% sucrose (by weight) (sucrose) (glucose) (glycerol)

440,000

17,900 412 416 420 350,000

421 -

ATPase a subunit Catalase

Matchpoint solution composition

58,000 425 248,000 425

330,000

427

330,000 427

I

(sucrose) (NaBr) (sucrose) (glycerol sucrose NaCl)

-

I1551

The spatial correlations between crystallins, however, reduce I ( 0 ) to 2.5% of that for the independent scatterers model. Thus interparticle interference accounts for the transparency of the eye lens, whch otherwise would be turbid [145]. 4.2.8. X-ray contrast variation and anomalous scattering X-ray contrast variation studies require solutions of up to 80% sucrose or 90% glycerol, or salt solutions of various molar concentrations, in order to adjust the contrast difference Ap over a suitable range (Table 9). It is necessary for the structure of the solute to be unaffected by these additives. Several proteins have had their electron matchpoint densities determined from plots of ( I (O)/ctT,)'/* against solvent electron densities [146-1551. The summary of Table 9 shows that these range between 398-427 e . nm-3. Initial comparisons with electron densities calculated from volumes based on amino acid densitometry, protein densitometry or protein crystallography to follow [37] show that these are best predicted from the latter set of volumes, which correspond to the actual physical volume occupied by the

205

macromolecule. Thus taking myoglobin, catalase and bovine serum albumin as examples, the calculated electron densities are 412 e . nm-3, 418 e . nmP3 and 420 e . nm-3 in that order. If an electrostricted hydration shell of 0.3 g H,O/g protein [37] (where a water volume of 0.0245 nm3 is used in place of 0.03 nm3) is included with the crystallographic residue volumes, similar electron densities of 411 e . nm-3, 416 e.nm-3 and 418 e - n m - 3 are obtained. T h s similarity reflects the hgher electron density of bound electrostricted water molecules (408 e . nm-3) in comparison to that of free water (334 e . nmP3). Electron densities are thus best understood in terms of the total volume of the protein and its electrostricted (denser) water shell (S.J. Perkins, unpublished calculations). Use of the consensus densitometric volumes for proteins to follow the classical Cohn-Edsall procedure [37] gives values of 431 e . nm-3, 442 e . nm-3 and 440 e . nmp3 which are too high. This occurs because these volumes have been affected by the electrostricted water shell surrounding the protein, which has the apparent effect of reducing the total protein volume [37]. Generally the fluctuations of X-ray scattering densities within the particle are small and usually not detectable. Thus the X-ray Stuhrmann a for malate dehydrogenase was (5 k 9) X lo-' [148], where the large standard deviation arose from poor signal-noise ratios. Its value is comparable with neutron a values. Model calculations using crystal structures for several globular proteins have shown that the protein R , as observed in positive contrasts in aqueous solution will exceed the R , of the protein shape by up to 6% for reason of the arrangement of surface hydrophlic residues and core hydrophobic residues [156,157]. X-ray contrast variation has been best applied to the metalloprotein ferritin, which consists of a mineral iron core (electron density 1000 e . nmP3) surrounded by a spherical protein shell (410 e . ~ ~ r n -of~ )24 regularly-arranged subunits [149,158-1601. The protein shell was matched out in 53% sucrose (w/w) or 0.66 g sucrose/ml solution, leaving the observed scattering to be caused only by the iron core (Fig. 17). Control experiments were performed on apoferritin which lacks the iron core [149,160]. Thus the R , for native ferritin is 3.7 nm, that of apoferritin is 5.6 nm and that of the iron core is 2.9 nm [158-1601. The outer and inner radii of the protein of ferritin were found to be 6.3 and 3.55 nm [160]. The radius of the iron core was found to be 3.66 nm and corresponded well to the scattering from a uniform sphere [149], rather than to other models based on a collection of spherical micellar domains that were proposed from electron microscopy studies (Fig. 17). Anomalous X-ray scattering leads to a different approach to contrast variation [17]. The scattering length of an atom f (in electrons here) is defined in this context as:

-

f=fo

+ A f ' + iAf"

where fo is the scattering length at zero wavelength and is equal to the number of electrons at zero scattering angle. Af' and A f " depend on the X-ray wavelength h and are the dispersion and absorption components of f . The dispersion effect A f ' is in phase with fo while the absorption effect A f " is out of phase by m/2. Both A f ' and A f " are large when h is close to an atomic absorption edge caused by

Q

(nm-’)

Fig. 17. X-ray contrast variation studies of ferritin (1491. Left: Apoferritin in 0.2 M phosphate buffer at pH 6.8 was studied to show that it could be modelled as a 0.6 hollow sphere of radius 6.1 nm (1. Contrast variation showed that this matched out in 53% sucrose. Right: Full ferritin in a 53% sucrose solution in which the scattering is dominated by the iron micelle and the protein component has been matched out. The solid line represents the theoretical scattering from a uniform sphere of radius 3.66 nm.

electronic excitation processes. A f’ becomes large and negative through the edge while A f ” jumps from below to above through the edge. In practical terms A f ” is measured from the sample absorption as X is varied through the edge, and the dispersion term A f ‘ is derived from A f” by the Kramers-Kronig relationship. As a general illustration of anomalous dispersion effect, solute-solvent contrast variation can be achieved by exploitation of the dependence of f (and hence scattering densities) on X through the edge. Using ferritin as a model [17,161], changes in scattering densities can be obtained (a) in the iron core by working near the K-edge of iron (A=O.1743 nm), and (b) in the solvent by using a 30% caesium chloride solution of ferritin and working near the L,-edge of caesium ( A = 0.2473 nm) (Fig. 18). Thus synchrotron radiation is required for this work since it offers a wide range of tuneability of A. T h s enables R , values to be measured as a function of A. At these edges, f for Fe varies by 7 electrons (out of 26) and that for Cs varies by 15 electrons (out of 55). In anomalous contrast variation experiments based on the solute, scattering densities are written as (see Section 2.7): p ( r , - PS = A p ‘ P V (‘)

+ P F ( r ) + ( Ap’ + A P ” ) p A ( r ,

where there are now regions defined by the step function p A ( r ) within the volume p v ( r ) where anomalous scatterers contribute to p ( r ) - p s . The dispersion and absorption terms are denoted by Ap’ and Ap”. For the anomalous scattering of the solvent, the boundary of the solvent coincides with that of p v ( r ) , so here: p(r)

-

ps = ( A P + AP’

+ iAp”)pv(r) + PF(T)

207

44t

2 4 7 3 nm

h,r01743 n m ? +

6

5

5

-

a0 4

2 5

-0.01 - 0 0 0 5

0

0005

3

-0002

0

0002

&Ak __

A,

Fig. 18. Anomalous contrast variation experiments using ferritin with synchrotron radiation of varying wavelengths [17]. Left: Dependence of the apparent R, of ferritin (+) on the wavelength h near the K-absorption edge of iron at A, = 0.1743 nm. The R, dependence follows that of the dispersion curve of A f ’ () where A f ’ is calculated from the absorption spectrum of ferritin (-----) by the Kramers-Kronig relation. Right: Dependence of the R, of ferritin ( + ) for a 3% ferritin solution in 30% CsC1. The increase of the R, is due to a decrease in the solvent scattering density near the Cs L, absorption edge at A,, = 0.2473 nm.

If Ap‘, Ap” G Ap, the Stuhrmann equation takes the form

Hence RG depends on the dispersion effect Ap‘ and not on the absorption effect Ap”. For a spherical structure where P = 0, the relative change of R G with X is a linear function of the decrease in Ap‘. For ferritin at the Fe absorption edge, the decrease in A f’ and Ap’ causes ferritin to lose electron density in the iron core and the R , rises by 4% or 0.2 nm to a sharp peak as X is varied through the edge (Fig. 18). For ferritin in 30% CsCI, the electron density of the solvent is 400 e . nm-3 which is very close to that of the protein component, so the iron core is primarily observed. At the Cs absorption edge, the solvent density is reduced. RG increases by 0.3 nm in reflection of the joint contribution of the protein and iron components to the observed R, value (Fig. 18). In both cases, the dependence of RG on X follows the same dispersion curve as that for Af’. 4.2.9. Label triangulation of heavy metal probes Some model experiments have been carried out based on the use of label triangulation of heavy metal markers [51,162,163]. Using a related nomenclature to Section

208

2.8, I ( Q ) of the unlabelled protein is denoted as Ill and that for the labelled where I,, is the scattering from the markers and I,, is the protein is Ill IZ2 Ilz, cross-term. The experimental procedure is based on the subtraction of the curve for the native protein from that of the labelled protein to give an oscillatory curve whose periodicity gives the required distance between metal sites. The subtraction assumes I,, to be negligible; test calculations show that there must be > 200 electrons in each marker for a protein of M, 100,000 for t h s to be a satisfactory approximation. Thus the distance between the tetra-mercury markers attached to Cys 93 in the two p chains of haemoglobin was determined as 3.8 0.2 nm, in good accordance with a calculation of 3.76 nm from the crystal structure [162]. The distance between mercury labels on histidine decarboxylase was determined as 6.9 f 0.3 nm [162]. The corresponding anomalous label triangulation method using synchrotron radiation has been applied to investigate the four Fe atoms of haemoglobin [164]. There will be a depression of about 5 electrons of the 2000 electrons in excess of solvent at the Fe K-edge, thus the relative intensity changes are of the order 0.001-0.01 of the total small-angle scattering. In practical terms, only the scattering from the non-iron atoms I,( Q ) and the cross-term IVA( Q ) is measurable, since that due to the iron atoms alone, IA(Q), is that of Iv(Q). Spherical harmonics were used to analyse Iv(Q) and IvA(Q) in terms of multipoles to suggest that the curve is dominated by the tetrahedral symmetry of the subunit structure and the iron structure, and that the distances between the iron atoms is about 2.6 nm. The two terbium sites in parvalbumin have also been analysed by anomalous label triangulation, based also on the terms in I,(Q) and IVA(Q)[165].

+ +

4.3. Neutron studies on globular proteins

The practicality of neutron scattering for proteins results from (a) the occurrence of matchpoints in the range of 40-45% 2 H 2 0 (Table lo), in relation to the high incoherent scattering background in H,O buffers and the low background in 'H,O buffers, and (b) the globular, ellipsoidal shapes of many proteins (Fig. 12). This means that while signal-noise ratios are significantly weaker in H,O and require counting times at least an order of magnitude greater than in 'H20, it is nonetheless feasible to acquire data over a large positive and negative contrast range. The two main applications of neutron scattering are consequently (a) investigations of overall shapes and their internal structures by contrast variation, and (b) label triangulation of deuterated subunits in multimeric proteins. 4.3.1. Contrast variation studies Neutron experiments were first made on haemoglobin [98,99,147,166,167] and were extended to myoglobin [44,168], lysozyme [169] and catalase [170] as models of typical globular proteins. In parallel with X-ray scattering, the haemoglobin work (mainly in 'H,O) identified a conformational change between the oxy- and deoxyforms which was reflected in an R , difference of 0.054 nm in 'H,O buffers. Scattering curve comparisons to Q = 3 nm-' with the crystal structures verified this.

209

TABLE 10 Summary of neutron data for proteins and metalloproteins analysed by Guinier R , and I ( 0 ) plots and Stuhrmann R,-, a and p plots. These are arranged in order of increasing neutron matchpoint. In general p is not measurable with accuracy; /3 values of 3X1O-l4 nm-’ (myoglobin) and 4 ~ 1 O - lnm-2 ~ (lysozyme) have been reported [44,169] Mr

Composition

Experimental matchpoint (%2H20)

R , (nm)

a( X

Ref.

Proteins

+-3.5

[441 ~ 7

Positive Positive

42.5 43 44.7

3.84 4.4 4.24 1.46 3.7 1.385

[181] [177] [178] [175] [170] [169]

92% protein 8%calcium phosphate

40.7

6.40

- 36

100% protein Protein/FeOOH

41

5.15

-0

~721

42 46 54 56

5.10 4.90 4.80 4.76

- 17

~721 ~721 ~721 [1721

Myoglobin Haemoglobin Mo-Fe nitrogenase Fl -ATPase

17,900 64,500

100% protein 100% protein

40.2 40.5

1.48 2.5-2.6

220,000 320,000

100% protein 100% protein

41 42

Ribonuclease A Catalase Lysozyme

13,700 248,000 14,300

100%protein 100% protein 100% protein

Casein

250,000

Apofemtin Ferritin 6% Fe saturated 45 %

440,000

-

+13k2

Positive Positive +3.5

1

Metalloproteins

85% 95%

- 70 - 140

- 140

11731

The RG values were higher by X-rays than by neutrons. In the classic neutron and X-ray contrast variation study on myoglobin by Stuhrmann (Fig. 19a) [44], the R , values were again higher in positive contrasts than in negative contrasts. These were now explained in terms of the internal structures, i.e. the hgher scattering density of surface hydrophilic residues compared with the lower scattering density of buried hydrophobic residues. Similar results were obtained for catalase and lysozyme. In the Stuhrmann equation, the centre of gravity of scattering density fluctuations is coincident with that of the shape of the protein to a good approximation, thus the term in p / A p 2 can be set as zero. The values of a from Stuhrmann plots thus quantifies the radial distribution of scattering density fluctuation. From the definitions of Section 2.7, a for a globular protein can be predicted from its proportionality to R L , noting that RG is also proportional to Mp.365 (Fig. 12). Values of a are given in Table 10. The extension of neutron contrast variation to the iron-protein ferritin (Section 4.2.7) illustrates polydispersity effects on small angle scattering [171,172]. For 6 0 4 0 % iron-saturated ferritin, the matchpoint graph of against % 2 H 2 0is not linear at low contrast differences A p , and I ( 0 ) does not become zero (Fig. 19b). This is attributed to variable iron contents in different ferritin molecules. In 42%

{m

210

h

0 L

0

0

40

80

0

40 Volume 01.

80

0

40

80

‘H,O

Fig. 19. Dependence of Z ( 0 ) on the volume fraction of H,O and 2 H 2 0 present in neutron scattering experiments. The vertical scales in (a), (b) and (c) are not to the same scale. (a) The values for myoglobin in 10 different contrasts are a linear function of the solvent scattering density [MI. This is the usual result of neutron contrast variation and indicates the monodispersity of the sample. The matchpoint corresponds to the so-called “dry” unhydrated volume of the protein. Typical Stuhrmann plots for proteins and glycoproteins are exemplified in Fig. 21. (b) The Z( 0) values for ferritin in 10 different contrasts are not linear when close to the matchpoint and Z ( 0 ) does not have a minimum value of zero. This is attributed to the polydispersity of the sample, where different molecules have different iron contents [171]. (c) The values for apoferritin [172] are plotted against the scattering density of the solvent. On adding various small-molecule solutes at 400 mg/ml to the solutions in either 0 or 100% 2 H 2 0 , such as urea, glycine, proline, glucose and sucrose, the solvent scattering density is changed. The values (0)show a linear dependence on the contrast. In distinction to the experiment of (a), the effective volume of apofemtin is larger since these solutes are unable to penetrate the hydration shell of apoferritin. The slope of the graph is thus higher than that from ordinary H , 0 - 2 H , 0 contrast variation (0),and the matchpoints from these correspond to the “wet” hydrated volume.

s ‘

,H,O when the protein shell is matched out, the R , of the iron core is 2.8 nm, in good agreement with the X-ray study. The iron core matches out at 90-100% 2H20. The Stuhrmann plot gives large negative a values in reflection of an iron core of higher scattering density than the protein shell (Table 10). Since a is obtained primarily from data at high Ap, polydispersity effects on a are minimal. As the iron content is reduced, a tends to zero. The Stuhrmann plots are linear ( p = 0) for different iron contents, except in that some curvature ( p f 0) cannot be ruled out at half iron-saturation. This suggests that the spherical iron micelle can be nrn-,, a asymmetric with respect to the protein shell. From a /3 value of separation of 0.2 nm was estimated between the centres of the iron micelle and the protein shell, which can be compared with the overall diameter of 12.6 nm. Similar experiments have been carried out with casein micelles and submicelles (92% protein; the remainder is mainly calcium and phosphate) [173]. A negative a was again found in Stuhrmann plots (Table lo), probably implying that the inorganic component is close to the centre of the casein molecule. Contrast variation can also be achieved by adding small molecules at 200-400 mg/ml concentrations such as sucrose, glucose or urea to the protein in H,O or in ,H,O [172,174,175]. For iron-free apoferritin [172], linear relations of with

-

/m

21 1

solvent scattering densities are again observed (Fig. 19c). This time, their slope is significantly increased. This is attributed to larger effective volumes caused by the inability of the small molecules in the solvent to penetrate the hydration shell on the surface of apoferritin. Note that the small molecules are able to penetrate the central cavity of apoferritin. An effective solvation of about 0.3 g H,O/g protein was calculated, and the R , was increased by 0.3 nm relative to ordinary H,0-2H,0 solvents. Similar experiments were carried out on ribonuclease using a range of ethanol-,H,O and gly~erol-~H,Omixtures [175]. Interestingly, that slope observed with ethanol is similar to that of ribonuclease in H,0-2H,0 and corresponds to a zero solvation effect within error, while that for glycerol is increased and corresponds to about 0.23 g H,O/g protein. In the latter case, the R G of the hydration shell could be estimated as 2 nm, in comparison to a protein RG of 1.4 nm. The difference between ethanol and glycerol is attributed to the ability of ethanol to bind to the protein surface. Similar experiments were carried out on halophilic malate dehydrogenase, which is stable only in high salt concentrations. Here, the R , of the hydration shell was estimated as about 4 nm, while that for the protein alone is 2.8 nm [148,176]. Neutron scattering has been applied to other protein systems. The shapes or properties of several systems have been investigated, namely the soluble BF, factor and the OSCP subunit of ATPase and the ATPase inhibitor [177-1801, the Mo-Fe nitrogenase [181], the giant haemoglobin of earthworms [182], and spectrin [183], the aggregation of superoxide dismutase [184], the contrast-dependent shape of ribulose bisphosphate carboxylase/oxygenase [185], actin dimerisation [ 1861, the blood platelet factor 4-heparin complex [184], and interparticle interference effects in bovine serum albumin [188-1901. Several of these studies record high contrast I(Q) data to large Q in only H,O and ’H,O solvents. Usually the RG is larger in H,O buffer than in ,H,O buffer in accordance with a positive Stuhrmann a (Table 10). In addition, the I ( Q ) curves at large Q can differ in these two contrasts. Simple triaxial bodies or assemblies of spheres are used to account for the scattering curve in these two contrasts [185]. These will include some minor changes to accommodate the differences seen in each of H,O and ,H,O solvents. An alternative and more satisfying procedure would be to calculate the experimental scattering curve at infinite contrast Iv(Q) for modelling purposes. In this sense modelling by neutron scattering offers an advantage over that by X-ray scattering, since the influence of internal structure fluctuations can be explicitly discounted from the shape, and in addition information is provided on the distribution of hydrophilic and hydrophobic amino acids [37]. Furthermore, radiation damage effects on the protein are avoided by the use of neutrons in preference to X-rays [184]. 4.3.2. Label triangulation and deuteration Label triangulation using deuterated proteins within a multimeric protein structure was first applied to DNA-dependent RNA polymerase (a2/$3’a)[52,191-1941 to follow the earlier X-ray studies on it. Totally-deuterated subunits (matchpoint equivalent to 120% ,H,O) were employed in a protonated matrix, and data were collected in 42% ,H,O. The subunits were prepared with deuterated algae extracts

-

212

as carbon source. This procedure minimises the effect of internal structure fluctuations p F ( r ) (Table 3) on the measured R , values by maximising the contrast difference A p between the labels and the solvent and simultaneously matchng out the protonated matrix. Firstly, the RG, values for each monolabelled multimer were measured in situ for each of a 2 , P, P' and a in 42% 2H,0. Next, for the a2-P, a2-/3' and P-P' distances, the RG values of (a) the mixture of bilabelled and non-labelled multimer and (b) the mixture of the two mono-labelled multimers were measured separately. The difference between (a) and (b) gave the required hypothetical RG12 value whch eliminated inter- and intra-molecular interference effects. Thus the centre-to-centre distance A was derived from the simple expression [53,191]: 2R&,

= R2G1

+ RL2 + A2

In addition, A was obtained from the Parallel Axes Theorem (Section 2.6) using individual R , data for the monolabelled and bilabelled multimers [191,192]. The u-a2, u-P and a-P' distances had to be obtained from the use of separate measurements of bi-labelled, mono-labelled and non-labelled multimers in dilute mono-disperse solutions, since the rapid exchange of the a subunit precluded the use of a mixture of bi-labelled and non-labelled multimers [193]. Thus far, only the Guinier regions have been analysed. The use of the curve I ( Q ) to Q = 1.3 nm-' leads to the A I ( Q ) curves. These difference curves, however, show strongly damped oscillations (cf. Fig. 6) for reasons of the highly elongated shapes of the a2. /3 and p' subunits, all in close contact with each other. The corresponding distance distribution functions D(r ) were also calculated [192,193]. These were compared with trial-and-error model calculations for various assemblies of elongated subunits to arrive at a self-consistent low-resolution description of the subunit arrangement which is shown in Fig. 20 [193]. In a further study of the interaction of the RNA polymerase with DNA, a deuteration procedure with 46% 'H20 growth media containing protonated glucose has been developed to give protein that will match out with DNA in 65% 2 H 2 0[194]. A different strategy was used to analyse the protein subunit structure of tryptophan synthase ( a 2 & ) [195], which also followed X-ray work. This was done by determining the three basic Dv(r), D F ( r ) and D v F ( r ) functions of contrast variation: D ( r ) = A p 2 . D v ( r )+ A p - D v F ( r )+ D F ( r )

The subunits were 70% deuterated, and this corresponds to a matchpoint of 89.5% 2H,0. All the preparations thus match out in the range between 40-90% 'H20, and this enables I ( Q ) to be measured to Q = 1.4 nm-' in at least 4 positive and negative contrasts. D ( r ) was then calculated and decomposed into the three basic functions. In turn the D ( r ) at each matchpoint can be calculated and interpreted in terms of the subunits under study. Thus the shape change on the formation of a2p2from the free a and ,B2 subunits (Section 4.2.5) [122] was located in p2 and not in a. The a

213

Fig. 20. Label triangulation of DNA-dependent RNA polymerase. The tetrahedron of centre-to-centre distances A between the four subunits a2,P, P’ and u was determined from the refinement of the R , measurements and the D ( r ) calculations. The following A values were obtained: P-P’, 6.5 nm; a,-P’, 7.5 nrn; a 2 - P . 7.0 nm; u - a 2 , 8.4 nm; o - p , 4.4 nm; 6 - p ’ , 10.7 nm. Eirors lie in a range of f0.2-2.2 nm.

subunits were positioned at the extreme boundaries in a2P2 and cleanly separated from each other with the P2 subunit sandwiched between them. Deuteration was also used to investigate the dimer of methionyl-tRNA synthetase [196]. Mixture of the deuterated and protonated dimers DD and HH causes hydrid HD dimers to be formed through reversible dissociation. The equilibrium mixture of HH, DD and HD dimers is polydisperse in a /l(o>matchpoint graph (cf. ferritin in Section 4.3.1) from which the amount of HD present is calculated. Comparison with the R , values measured as a function of percentage 2 H 2 0 gave the R , of the monomer and the Parallel Axes Theorem gave the distance between the monomers. 4.4. X-ray and neutron studies on glycoproteins

The glycoproteins considered here possess short carbohydrate chains on the surfact of a globular protein core. Almost all the glycoproteins studied by solution scattering to date originate from human plasma. These include immunoglobulins, protease inhibitors, acute phase reactants, and components of the clotting and complement cascades. The carbohydrate chains can be either the high-mannose type or the complex type that are N-linked to Asn residues, or shorter forms that are 0-linked to Ser or Thr residues (or in rare instances to hydroxylysine residues). 4.4.I . Plasma glycoproteins, proteoglycans and polysaccharides

Several glycoproteins have been studied as models containing globular protein cores and surface carbohydrate chains, mostly by neutron scattering. These are a1 acid glycoprotein (44% carbohydrate) [197,198],transcortin (27% carbohydrate) [199] and transferrin (6% carbohydrate) [200,201]. The neutron matchpoints are 44.7%, 42% and 40.5% 2 H 2 0in that order. Since carbohydrate chains on the protein surface are relatively distant from the scattering centre of mass, R , measurements provide a useful monitor of whether or not the chains extend freely into solution or are folded

TABLE 11 Summary of neutron data for glycoproteins and related macromolecules based on Guinier and Stuhrmann analyses. The glycoproteins subsection is arranged in order of increasing neutron matchpoint. Values of /? are not measurable, although one of 80+40X10-14 nm-’ has been suggested for half-a, macroglobulin [212]. Mr

Glycoproteins Transfemn

Transcortin Platelet factor 4heparin complex Fibrinogen Half-a, macroglobulin Link protein Hyaluronatebinding region al acid glycoprotein

% Carbohydrate (by weight)

Experimental matchpoint (% ,H,O)

R , (nm)

75,000

6

40.5 kO.5

3.03 f 0.05

52,000

27

42

2.36

45,200 340,000

31 3

42 k 4 42.5

360,000 42,000

10 4

43 43.2

67,000

25

43.8, 45.1

37,000

44

43-45

2.05 f 0.1 10.8

RG Rxs RG RXS

5.80k0.03 2.9 k0.2 0.8 k0.2

a(~10-5)

Ref.

-

[2001

22

[I991

25 f 10 -0

~ ~

7 4

1 1

9k 3 -0 -0

PI21 ~ 4

1

~

1

5.1 f0.2 -0 1.86 + 0.04 30+ 2.37 f 0.03 27k (native, high salt) 43k 2.84 k 0.04 (biantennary, high salt) 7* 2.24 f 0.03 (tri-tetraantennary, high and low salt; biantennary, low salt)

4 2 4 2

4

[197,198]

Immunoglobulins

IgG

150,000

2

41

IgA (MOPC315)

169,000

8

40.8 f 0.6

53,000

0

41.6 +0.4

45,500

0

44.2 f 0.2

IgA (MOPC315) Fab fragment Bence-Jones protein Mcg Complement Clq Clr,Cl s

41.5 43 43.3 f1 40.4

c3

460,000 350,000 810,000 193,000

c3c

143.000

6

40.7

38,800

0

39.3

c1

C3dg

,

7.2 kO.1 2.1 +O.l 1.2 +O.l 7.72 f 0.07 2.25 + 0.08 1.32 + 0.07 2.74 0.04 1.29 f0.08

+

5

2.40

12.8 17 12.6 5.1 2.4 4.8 2.0 2.7

-0 -0 -0 -1* 20 -9+ 7 -3+ 2 -7+ 5 3+ 2

k0.2 +2 +0.2 +0.1 +0.1 kO.1 *O.l +0.2

-100+100 Positive look 100 30+ 10 lo* 10 20+ 10 15+ 5 35+ 10

216

Native

-

:@

5

4

-50

0

50

-50

1

I

0

50

I

-50

I

!

0

5C

A> ( ~ 1 0nm2) '

Fig. 21. Stuhrmann plots of R& u . A p - ' for a, acid glycoprotein in buffers containing 1 M NaCl (0) and 0.2 M NaCl (0).The native preparation is a mixture of the biantennary and tri-tetraantennary forms. The unfolded configuration of carbohydrate chains occurs in 1 M salt for the biantennary form; the folded configuration is found in 0.2 M NaCl for both forms and in 1 M salt for the tri-tetraantennary form. Since the Stuhrmann plots for the folded and unfolded forms intersect at negative A p - ' values, it is concluded that the hydrophilic part of a, acid glycoprotein (i.e. the carbohydrate) with the higher scattering density is implicated in the conformational change. The hydrophobic protein core with the lower scattering density is dominant in the Stuhrmann plot at negative A p - ' (70-100% 'H,O buffers) and the R& values are similar in both 0.2 M and 1.0 M salt buffers. Computer models for a1 acid glycoprotein using spheres of 0.608 nm diameter are shown for the biantennary form at high salt and for the tri-tetraantennary form [198].

against the protein core surface. T h s can be judged by comparison with Fig. 12 for the RG of globular proteins (Section 4.2.1). RG values significantly larger than expected from the M , value would suggest that a hypothesis of extended carbohydrate structures should be investigated. The value of a for glycoproteins tends to be larger than those for non-glycoproteins (Tables 10 and 11). This reflects the surface disposition of carbohydrate residues with higher scattering densities than those in the protein core. More direct evidence of carbohydrate structures was obtained in neutron studies of native a1 acid glycoprotein from the observation of an unusual conformational change on increasing the NaCl concentration from 0.2 to 1.0 M [197]. Since carbohydrates have a higher matchpoint of 49% 2 H 2 0 relative to that of 42% 2 H 2 0 for proteins, the method of H 2 0 - 2 H 2 0 mixtures was used to show that the conformational change occurred in the carbohydrate moiety and not the protein (Fig. 21). The native preparation was purified and separated into two fractions, one containing only biantennary complex-type carbohydrate chains and the other containing only tri-tetraantennary chains. Further NaC1-dependence studies showed that the conformational transition occurred only in the biantennary form (Fig. 21)

217

[198]. As shown in the Stuhrmann plot of Fig. 21, contrast variation indicated that the carbohydrate component and not the protein component underwent the conformational change (Table 11). Molecular modelling of the two preparations showed that in low salt, both forms had compact structures of carbohydrate folded against the protein core, while in high salt the carbohydrate chains of the biantennary form extended into solution. The general conclusion of these studies is that glycan chains are usually folded into compact arrangements with protein surfaces under physiological conditions, and that conformational heterogeneity can be associated with carbohydrate sequence heterogeneity. Solution scattering studies have also been reported for the blood clotting precursors, fibrinogen (X-rays and neutrons) [202-2051 and prothrombin (X-rays) [206], and for the protease inactivator a,-macroglobulin (X-rays and neutrons) [207-2121, all of whch are human plasma glycoproteins with elongated shapes. The RG values are 10.8-14.2 nm for fibrinogen ( M , 340,000), 3.6-4.0 nm for prothrombin ( M , 74,000), and 7.2-7.8 nm for a,-macroglobulin ( M , 710,000). The studies with a,-macroglobulin have included titration studies with its substrate, trypsin (from which the formation of a 1: 2 inhibitor-trypsin complex could be inferred) [208], modelling in terms of a hollow cylinder [207,208,210], X-ray contrast variation (see Table 15) [209], temperature-dependent properties [211], and cleavage into half-molecules with an R, value of 5.7 - 5.8 nm [212]. Glycoproteins from proteoglycans of cartilage have been studied by X-ray and neutron scattering [213,214]. A survey of scattering densities for carbohydrate and protein residues was presented in [213], and this has recently been updated [37]. Two slightly-elongated macromolecules that interact with hyaluronate polysaccharide chains in cartilage were characterized, namely binding region (25% carbohydrate) and link protein (4% carbohydrate). The elucidation of their interaction in their ternary complex with hyaluronate was also studied. Binding region constitutes a distinct structural type of glycoprotein in that a carbohydrate-rich domain was identified from the large value of a in R,, analyses but not from the R, analyses in Stuhrmann plots (Table 11).This reflects the disposition of carbohydrate on the outer edge of the long axis of the macromolecule and protein at the centre of this long axis. A further interest of this work was the control of non-specific self-aggregation problems which otherwise affect the success of Guinier RG analyses [214]. In general, the use of *H,O buffers or synchrotron X-ray beams encourages aggregate formation and these are best avoided by working in H,O buffers by neutron scattering. However, where trace amounts of aggregates are unavoidable, these can be suppressed by the use of 2-methyl maleyl anhydride to modify the surface lysine groups, as was employed in the cases of binding region and link protein. X-ray and neutron scattering has been applied to a number of neutral and polyanionic polysaccharides, namely starch granules [215,216], heparin [217-2201, amylose [221], hyaluronic acid [213], and chondroitin sulphate [213]. Neutron matchpoints were reported for starch (50% 'H,O), hyaluronate (51% 'H,O) and chondroitin sulphate (60 k 5% ,H20). Both types of polysaccharides are usually analysed in terms of extended worm-like chain structures in solution. Data are commonly represented as cross-sectional R,, values (typically around 1 nm) and

218

[ I ( Q ) .Q]Q+o values. Persistence lengths (typically 1-6 nm) are obtained from Kratky plots of I( Q ) Q 2 against Q, and are given by the intersection of the regions where Z(Q) a Q-’ (at intermediate Q ) and Z(Q) a Q-’ (at large Q) [217-2211. For short polysaccharides, R , values reflecting the overall length of the chain can be measured. 4.4.2. Immunoglobulins Immunoglobulins recognize foreign material and constitute the largest group of glycoproteins to be studied by solution scattering, although investigators have not usually made an explicit consideration of the carbohydrate moiety in their analyses. Work has included the major IgG, IgM and IgA classes of immunoglobulins as well as the Bence-Jones proteins. Typical carbohydrate contents are 2-3% for IgG, 8-12% for IgM and 7-11% for IgA. X-ray and neutron scattering studies on IgG [222-239; reviewed in 13,74,235]have examined the following aspects: (a) identification of the shape of intact IgG [222,226,228,232,236,237,239];(b) comparison between the IgG subclasses [232,239];(c) study of structures and possible conformational changes on the addition of hapten or antigen [223-226,229,231,233,234,2361; (d) comparisons of IgG and its fragments with crystal structures [227,228,238]. Similar themes apply to work on IgM [240-2431, IgA [244] and Bence-Jones proteins [245]. The results from the IgG studies can be summarised as follows. (a) Intact, homogeneous IgG is characterized by overall R , values in a typical range of 6.0-7.5 nm and additionally by two distinct R x s values in the ranges of 2.1-2.5 nm and 1.1-1.5 nm (Table 11). The first R x s range corresponds approximately to the shape of the IgG hinge and Fc domain, and the second one to that of the average cross-section of the Fab domains (Fig. 22). Analyses were facilitated by the proteolytic disassembly of the IgG molecule into its Fab and Fc fragments [222,226,232,236].The complete scattering curve I( Q) corresponds to the well-known Y-shape of the IgG molecule. Computer modelling suggests that t h s adopts a T-configuration in solution, albeit a flexible one. (b) More recent work has explored the comparisons between the human IgG1, IgG2, IgG3 and IgG4 subclasses [232,239], where the IgGl, IgG2 and IgG4 subclasses are similar to one another in shape while the IgG3 subclass possesses an unusually long hinge between the Fab and Fc domains at the centre of the Y-shape. While one group has reported the anticipated larger R , of 8.4-8.6 nm for IgG3 [232], another group has reported a low value of 4.9 nm [239]. (c) Anti-poly-D-alanyl [224,226,234],anti-p-azophenyl-ppolyclonal antibodies have been lactoside [225],and anti-dinitrophenyl[229,231,236] raised and studied. Comparison of their scattering curves before and after the addition of their respective hapten or antigen suggests that the RG values contract by 2.5-8%. However, this contraction is not observed for the Fab or (Fab’), fragments [226], nor for IgG whose interchain disulphide bonds have been cleaved [234]. Despite these RG results, which at first sight would suggest an allosteric mechanism for IgG activation, IgG activation is nowadays accepted to proceed through associative mechanisms involving the presence of many adjacent IgG molecules in proximity. Other related studies have attempted to estimate the

219

0

0.20

0.40

0.60

0.80

Q ( nm-'1

Fig. 22. Comparisons of the expenmental neutron curve for C l q of complement in 100% 'H,O buffers with the calculated curves for three distinct Debye models for Clq, drawn using spheres of radius 0,595 nm. The C l q model used in the fit for curve A is shown to the right in two views. The calculated curve is corrected for polychromicity and beam divergence effects. The mean arm-axis angle of C l q is 40-45O, and this can fluctuate by as much as f 30 O , from equilibrium. Symmetric, rigid models for C l q do not fit the experimental data. Satisfactory curve fits were obtained by varying the six arm-axis angles by k25" (curve A), or the six arm-arm angles by +30° (curve B), or by taking a weighted sum of scattering curves from a series of symmetric, rigid C l q models (curve C). The success of these models imply that C l q is flexible in solution. A model of an IgG antibody is shown for comparison with the C l q model [250].

distance between the two Fab binding sites by use of an IgG(dextran), complex [233], using the Parallel Axes Theorem to give the distance between the bound antigens. (d) Human IgGl Kol has been crystallized as well as its (Fab'),, Fab and Fc fragments and atomic-resolution structures are available. Comparisons with experimental scattering curves show discrepancies in that while the shapes are generally similar, the solution structures are more elongated than the crystal structures or differ otherwise [227,230,238].Similar experiments based on the crystal structure of Bence-Jones protein Mcg, however, show that the R , values between the crystal and solution states are compatible [245]. In conclusion, while the general features of IgG scattering analyses are well understood, the studies have left a number of discrepancies which require critical reappraisal. 4.4.3. Components of complement The complement cascade constitutes a set of about 20 glycoproteins whch are activated sequentially by limited proteolysis in response to signals associated with the entry of foreign material into the circulation (including activated immunoglobulins IgG and IgM). X-ray and neutron scattering has been of value in elucidating the shapes of the individual components and the complexes formed between them [41,246-2521. High-flux beam sources are frequently needed in t h s work since several complement components are of limited solubilities.

220

C1 of complement is composed of two subunits, Clr,Cls, and Clq. Neutron scattering in 100% ,H,O showed that Clr,Cls, is rod-like, in accordance with electron microscopy results [247]. The C l q structure is most unusual, resembling six globular protein domains which are held together by six collagenous arms. The neutron curve to Q = 0.8 nm-' (Fig. 22) exhibits an unusual minimum at Q = 0.28 nm-' and a maximum at Q = 0.39 nm-' [246,248]. Debye modelling was able to account for these (Fig. 22). From the analyses of the R , values of native C l q and a modified form in which its six globular domains were removed, and from the position of the minimum at Q = 0.28 nm-', it was shown that the C l q collagenous arms are of length 14.5 nm in solution and not 11.5 nm as proposed from electron microscopy. The difference in C l q arm length is most probably due to the known shrinkage of collagen in vacuo, or to experimental errors in magnification in the electron microscope. From the curve fits of Fig. 22, it was concluded that the C l q heads are arranged in a flexible ring-like structure with a mean arm-axis angle of 40"-45" which can fluctuate by as much as f 3 0 " from equilibrium [250]. The complex of C1 between Clq and Clr,Cls, was also studied. Use of the Parallel Axes Theorem with the R , values from experiment and constraints fixed by the C l q model showed that Clr,Cls, underwent a major conformational change on binding to Clq [248,250]. Analysis of the I ( Q ) curve to Q = 0.8 nm-' in which the C l q minimum and maximum have now disappeared showed that the C1 curve can be accounted for in terms of a much-folded Clr,Cls, structure bound onto one side of the Clq structure. This suggests that Clq acts as a template for a directed folding of Clr,Cls, to bring together the catalytic centres of Clr,Cls, involved in C1 activation. Similar high-flux X-ray and neutron studies have been carried out for C3 [252] and the C4b binding protein [41] of complement. The strategy of refinement of electron microscopy models by scattering analyses have improved the structural understanding of these molecules. Thus C3 was previously believed to be spherical in shape. The scattering analyses was based on each of C3 and its two major fragments C3c and C3dg, and identified a lamellar structure in the solution state for C3 [252]. The self-consistency of the three models and their curve fits with experimental data is a good indication of the validity of the method. The difference with electron microscopy was attributed to,the observation of face-on views of C3 in the microscope. The C4b binding protein has a multisubunit structure composed of a bundle of rod-like cylinders connected together at one end. Scattering analyses showed that there were 7-8 subunits and that the cylinders were arranged in solution close to one another with an arm-axis angle of 10" [41]. Electron microscopy had suggested that the cylinders were splayed out with an arm-axis angle close to 90 ", probably the result of sample preparation artefacts. Immunoglobulins and complement components have structures that are much more elongated than those of globular proteins (Sections 4.2.1 and 4.2.2). In neutron work, the Stuhrmann a for several of these molecules have values that are close to zero and are sometimes negative (Table 11). These are lower than expected by analogy with globular proteins (Table 10). They can be accounted for in terms of these elongated shapes, within which the radial distribution of hydrophilic and

221

hydrophobic residues throughout the glycoprotein structure is necessarily more even, and the value of a is thereby reduced. 4.5. Lipids, detergents, membrane proteins and lipoproteins 4.5.I . Lipid vesicles and complexes with proteins Unilamellar lipid vesicles are prepared by ultrasonication of phospholipid dispersions of large multilamellar liquid crystalline aggregates. Vesicles are typically hollow with ranges of diameters at least of an order of magnitude larger than the thickness of the lipid bilayer shell ( - 5 nm). While the overall size and shape cannot be easily described by solution scattering, it is, however, possible' to investigate lamellar thcknesses and scattering length density distributions across the membrane bilayer [253,254]. The scattering curve can be modelled using an infinitely thin hollow shell where, for a radius of R , zero minima are observed at Q increments of T / R . Since vesicles are polydisperse, which corresponds to variations in sphericity or R , the minima are averaged out to leave only the scattering curve of the envelope. One theoretical treatment has considered the scattering curve to arise from a random assembly of flat sheets of the vesicle membranes. Improved treatments show that the scattering from curved vesicles is similar [255]. These solution studies should not be confused with the small angle diffraction studies of orientated multilayer specimens such as the myelin sheaths of nerves, the outer segments of retinal rods, layered purple membranes from Halobacterium halobium and those that are made artificially by flattening vesicles by centrifugation or by drying. Here a different methodology based on diffraction is employed, which is discussed elsewhere [256-2581. Scattering studies on lipid systems (reviewed in [75]) have investigated random dispersions of model phospholipids [254,259-2611, Mycoplasma laidlawii membranes [253,262] and dihexadecyl phosphate [263]. Typically, electron density profiles or distance distribution functions across the membrane are calculated. Alternatively Guinier analyses based on the R,, from the thickness scattering factor I( Q ) . Q 2 are employed. The X-ray scattering curve of the bilayer can be accentuated by labelling the membrane with UOt+ ions [264,265]. Neutron scattering, using deuterated phospholipids in conjunction with protonated phospholipids or cholesterol, and Guinier thickness analyses using only the [I(Q ) . Q2IQ parameter, is able to study the lipid phase diagram as a function of the ratio of lipids present and temperature [266-2691. Phase separation results in a polydisperse mixture of distinct species. The study of this as a function either of H,O :*H,O ratios or the deuteration level of one species in a given fixed 2H,0 buffer yields the characteristic curved matchpoint graph of polydisperse systems (Fig. 23). This graph becomes linear upon the formation of a single phase. Protein-vesicle systems have been studied also, such as the thylakoid membranes of the phototropic bacterium Rhodopseudomonas spheroides [270]. Thus the apolipoprotein C-III/phosphatidylcholine complex has been studied with X-rays to show that a single particle contains about 9 apo C-I11 and 454 phospholipid molecules, is smaller than the average parent phospholipid vesicle, and has a platelet-like shape ~

222

Fig. 23. Use of neutron contrast variation to examine lateral phase separations in liposomes composed of a 3 :7 mixture of deuterated DMPC (Table 6 ) and protonated DMPA (dimyristoyl phosphatidic acid) at 3OOC. The chain melting transition is 23OC. Thickness Guinier plots of I n ( I ( Q ) . Q 2 ) 0 .Q 2 were analysed to give values which are plotted as a function of the H 2 0 - 2 H 2 0 volume ratio. The mixture cannot be matched completely and the curve shows a minimum which indicates that phase separation has taken place [266]. If the components are miscible, a linear matchpoint graph will result [267].

{ s

[271]. A rhodopsin-lipid complex in hexane has been studied using X-rays [272]. This was analysed in terms of an inverted lipid micelle surrounding the protein. Neutron scattering has been applied to lipid systems containing cytochrome b, 12731, F,F, ATPase [274] and reaction-centre protein in photosynthetic membranes [275]. Three distinct approaches were employed. (a) Cytochrome b, was asymmetrically reconstituted into small lipid vesicles composed of a highly deuterated phospholipid (to increase the contrast with the protein), each on average containing about 110 protein and 1900 lipid molecules. Stuhrmann plots based on Guinier R , analyses gave the R , and a for the free and the complexed vesicles (Table 12). Comparisons with models for a in terms of concentric spherical shells suggested that the hydrophobic domain of cytochrome b, penetrated both the inner and outer monolayers of the vesicle bilayer. (b) The F,F, ATPase was also reconstituted into deuterated phospholipids, where the scattering curve to Q = 1.2 nm-' was measured in 84%'H20 (the phospholipid matchpoint) in an 6 : 1ratio of vesicles :protein. The scattering curve from the protein alone could be identified and modelled (although there will be a residual lipid contribution to the observed scattering curve in 84% ' H 2 0 for reason of scattering density inhomogeneities). (c) Thickness R,, Guinier analyses [275]have been applied to the photosynthetic membrane (3 : 1 protein : lipid) using contrast variation and the Stuhrmann plot, from which a was determined as 22 X lo-, (Table 12). The a value was accounted for in terms of a hydrophobic membrane core and hydrophilic outer surfaces in both the protein and lipid components. Repeating the experiments using only the reaction-centre protein of

TABLE 12 Summary of neutron data for protein-lipid systems based on Guinier and Stuhrmann analyses Mr

Composition (by weight)

Experimental matchpoint (% H 7 0 )

R,

(W

a (X lo-’)

B (X

nm-*)

Ref.

-

Protein -lipid

Cytochrome b, deuterated phospholipid vesicles Trypsinized cytochrome b, deuterated vesicles Deuterated vesicles Photosynthetic membranes

-

Lipid Lipid-Reaction centre protein

-

lipid:protein molar ratio =

78

16.5 f O . l

84

23.8 f0.2

106

14.6 fO.l

70

-

270 130

-

10

-

-4OOf

18:4 -

-

-

100%lipid

-

lipid:protein weight ratio =

30

RTH

1.45f 0.01

4:l 100% lipid

11.6

RTH

1.25f0.04

protein volume fraction 0.32 PVF of 0.27 PVF of 0.22

19.5 16.2 17

RTH

1.36f0.05 1.32rt0.02 1.28f0.02

1.9X lo6

79% lipid

15

8.0

2.3x lo6

79% lipid

15.5

79% lipid

17.5

RTH

RTH

*

70f

- 4.5( rt 6)

22

4

-

16f 2 9f 2 11f 2

-

9f

Plasma lipoproteins

Low density lipoprotein Low density lipoprotein Low density lipoprotein enriched 2.5 x lo6 in phosphatidylcholine-N(CD,)

280

0

7.73 0.05

*

190

0

7.86f 0.05

240

0

N h) W

224

the membrane gave a transmembrane length of 5.2 nm for the protein and a of about 12 X lo-’ (Table 12). 4.5.2. Detergent micelles and complexes with proteins Individual membrane proteins can be solubilized by the use of detergents, and the protein-detergent complex can be studied. This method requires monodisperse complexes (i.e the bound micelles should be of similar size and mass) and these are not difficult to prepare. Since the protein-detergent complex exists in equilibrium with free detergent micelles, the buffer background samples should contain detergent also at the equilibrium concentration so that the buffer curve subtraction will lead to the protein-detergent curve only. X-ray and neutron studies on free micelles have been reported for several detergents such as Triton X-100 [39,276,277], lithium dodecyl sulphate [278], Cemulsol [39,279], dodecyldimethylamine oxide (DDAO) [280,281], laurylamidodimethylpropylaminoxide (LAPAO) [282], sodium deoxycholate [283] and sodium taurodeoxycholate [284] (Table 7), often in conjunction with the study itself of the membrane protein. Most detergent micelles are oblate and not prolate ellipsoids [285]. Novel micelle systems have been studied by solution scattering. The solubility of cholesterol in bile (taurodeoxycholate) and lecithin mixed micelles has been investigated by X-ray scattering [286]. Chlorophyll-water micelles were studied in organic media by neutron scattering as a model for bulk chlorophyll in photosynthetic bacteria to show that these have elongated hollow cylindrical shapes [287]. X-ray scattering has been applied to the rhodopsin-DDAO complex [280], the ATPase-deoxycholate complex [283] and the reaction centre-DDAO complex [281]. For the rhodopsin-DDAO system, RG contrast variation analyses were carried out using 0 - 50% sucrose concentrations (Table 13) [280]. Importantly, sucrose has no effect on DDAO binding to rhodopsin; Triton X-100 cannot be used for this reason. A linear Stuhrmann plot was obtained from which it was deduced that the protein and micelle are centrosymmetric and that the micelle surrounds the protein. Contrast variation with the ATPase-deoxycholate system (Table 13) is of interest in that the electron densities of the protein and detergent moieties are similar [283]. This simplified the shape analysis of I ( Q ) in terms of the distance distribution functions D( r ) from data measured in ordinary buffers. A coaxial double-cylinder model gave a good fit to D ( r ) for this system. Neutron scattering has been applied to the following systems: rhodopsin-DDAO [279], rhodopsin-Cemulsol [279], colipase-taurodeoxycholate [284], acetylcholine receptor-Triton X-100 [276,288], ADP/ATP carrier protein-LAPAO [282], cytochrome reductase-Triton X-100 [39] and cytochrome reductase-Cemulsol [39] (Table 14). Neutron contrast variation permits the match-out of the detergent moiety, thereby permitting structural observation of the protein alone. Residual scattering inhomogeneities can be important since micelles lie on protein surfaces, thus maximising their influence on the observed protein R G . To minimize its influence, detergents can be made to be homogeneous in scattering densities by selective deuteration in the case of Cemulsol, i.e. using a mixture of fully-deuterated, half-deuterated and protonated detergents [39,279]. Alternatively, a detergent with a

TABLE 13 Summary of X-ray data analysed by Guinier and Stuhrmann plots Mr

Glycoproieins a,-macroglobulin

713,000

Composition by weight

Electron density (e.nm-3)

Matchpoint solution composition

R , (nm)

ol(e.nm-')

10%carbohydrate

412

55% sucrose (w/w)

8.0

- 640

Protein -detergent Rhodopsin-DDAO

81,100

52%detergent

356

16% sucrose

2.95

69

DDAO

16,700

100%detergent

312

- 17%sucrose (w/w)

1.84

87

ATPasedeoxycholate

134,000

15%detergent

407

67% sucrose (w/w)

3.7k0.1

High density lipoproteins Human LpA, Human HDL, Pig HDL,

186,000 175,000 210,000

42% lipid 45% lipid 56% lipid

381 367 375

4.2 4.06 4.1

280 243 -

Human LpA,

360,000

59% lipid

365

36% sucrose NaBr (0-7 M) Sucrose (0-80% W/W) Sucrose (0-65% w/w)

4.7

300

Low density lipoproteins Human LDL Human LpB

2.2 x lo6 2.4 X lo6

77% lipid 79% lipid

343 348

8.79 9.0

826 1300

3.1 X lo6

82%lipid

342

NaBr (0-7 M) Sucrose (0-55% w/w) NaBr (0-7 M)

8.98

1186

1.45 X l o 6

68% RNA

455

87% sucrose (w/w) (6-52% experimentally)

-

Monkey LDL, Ribosomes 50s ribosome

Ref.

Negative

-

Contrast variation with the use of 0.4-4 M (NH4)2S04 [505], 0-80% sucrose [506,508,512] or 0-32% melezitose [512] has been described in virus scattering experiments, but without the determination of the Stuhrmann parameters. The matchpoint of DDAO is hypothetical.

h,

b!

226

very small polar head can be used such as DDAO [279]. The more effective approach (used with rhodopsin and cytochrome reductase) is to use a hydrogenated and a deuterated detergent with matchpoints below and above that of the protein, and determining the Stuhrmann plot for each of the two detergent systems (Table 14). Intrapolation of the two plots at the appropriate contrast matchpoints for the protein and the detergent yields the R, and (Y for the detergent and the protein, respectively (Fig. 5c). In this way, the neutron and X-ray scattering models for rhodopsin could be compared [279,280]. For cytochrome reductase, the protein and detergent R , values could be identified for use in verification of the electron microscopy model for this enzyme as in Fig. 5c [39]. This procedure was repeated for the cytochrome bc, subunit-detergent complex of cytochrome reductase [39]. The use of one detergent only, as in a study of acetylcholine receptor-Triton X-100 [276], leads to too small an R , for the detergent moiety, and this is readily attributed to the effect of intern